From 113a50d08e6df39310a9b577c224677d1465e8d9 Mon Sep 17 00:00:00 2001 From: Simon Guichandut <40605210+simonguichandut@users.noreply.github.com> Date: Wed, 9 Aug 2023 19:56:12 -0400 Subject: [PATCH] Create incompressible_viscous solver and lid-driven cavity test problem (#138) Needed to change a few things in incompressible/simulation.py as well: Neumann BC's on phi in the case of dirichlet BC's on v (and apply phi-specific BC's in the multigrid solves) Allow user-defined BC's Allow another method for the velocity update in the evolve loop The latter two are then redefined in incompressible_viscous/simulation.py. The rest of the methods are inherited from the base class. For the lid-driven cavity problem, the only free parameter is the viscosity. Since the velocity and length scales are =1, the Reynolds number is just 1/viscosity. --- .gitignore | 3 + README.md | 3 + docs/source/cavity_Re100.png | Bin 0 -> 591294 bytes docs/source/cavity_Re1000.png | Bin 0 -> 685976 bytes docs/source/cavity_Re400.png | Bin 0 -> 642102 bytes docs/source/incomp_viscous_converge.png | Bin 0 -> 22657 bytes docs/source/incompressible_viscous_basics.rst | 115 +++++++++++ .../incompressible_viscous_defaults.inc | 36 ++++ docs/source/index.rst | 1 + .../pyro.incompressible_viscous.problems.rst | 42 ++++ docs/source/pyro.incompressible_viscous.rst | 34 ++++ docs/source/pyro.rst | 1 + docs/source/refs.bib | 30 ++- docs/source/shear_viscous.png | Bin 0 -> 109675 bytes pyro/analysis/incomp_converge_error.py | 7 +- .../analysis/incomp_viscous_converge_error.py | 57 ++++++ pyro/incompressible/incomp_interface.py | 75 ++++++- pyro/incompressible/simulation.py | 127 ++++++++---- pyro/incompressible_viscous/BC.py | 50 +++++ pyro/incompressible_viscous/__init__.py | 24 +++ pyro/incompressible_viscous/_defaults | 13 ++ .../problems/__init__.py | 1 + .../problems/_cavity.defaults | 1 + .../problems/_converge.defaults | 1 + .../problems/_shear.defaults | 4 + .../incompressible_viscous/problems/cavity.py | 42 ++++ .../problems/converge.py | 67 ++++++ .../problems/inputs.cavity | 31 +++ .../problems/inputs.converge.128 | 36 ++++ .../problems/inputs.converge.32 | 36 ++++ .../problems/inputs.converge.64 | 36 ++++ .../problems/inputs.shear | 35 ++++ .../problems/plot_cavity.py | 82 ++++++++ pyro/incompressible_viscous/problems/shear.py | 67 ++++++ pyro/incompressible_viscous/simulation.py | 190 ++++++++++++++++++ .../tests/cavity_n64_Re400_0025.h5 | Bin 0 -> 219089 bytes .../tests/convergence_errors.py | 37 ++++ .../tests/convergence_errors.txt | 6 + .../tests/convergence_errors_no_limiter.txt | 6 + .../convergence_errors_zero_viscosity.txt | 6 + .../tests/convergence_plot.py | 52 +++++ pyro/pyro_sim.py | 1 + pyro/test.py | 1 + 43 files changed, 1306 insertions(+), 50 deletions(-) create mode 100644 docs/source/cavity_Re100.png create mode 100644 docs/source/cavity_Re1000.png create mode 100644 docs/source/cavity_Re400.png create mode 100644 docs/source/incomp_viscous_converge.png create mode 100644 docs/source/incompressible_viscous_basics.rst create mode 100644 docs/source/incompressible_viscous_defaults.inc create mode 100644 docs/source/pyro.incompressible_viscous.problems.rst create mode 100644 docs/source/pyro.incompressible_viscous.rst create mode 100644 docs/source/shear_viscous.png create mode 100755 pyro/analysis/incomp_viscous_converge_error.py create mode 100644 pyro/incompressible_viscous/BC.py create mode 100644 pyro/incompressible_viscous/__init__.py create mode 100644 pyro/incompressible_viscous/_defaults create mode 100644 pyro/incompressible_viscous/problems/__init__.py create mode 100644 pyro/incompressible_viscous/problems/_cavity.defaults create mode 100644 pyro/incompressible_viscous/problems/_converge.defaults create mode 100644 pyro/incompressible_viscous/problems/_shear.defaults create mode 100644 pyro/incompressible_viscous/problems/cavity.py create mode 100644 pyro/incompressible_viscous/problems/converge.py create mode 100644 pyro/incompressible_viscous/problems/inputs.cavity create mode 100644 pyro/incompressible_viscous/problems/inputs.converge.128 create mode 100644 pyro/incompressible_viscous/problems/inputs.converge.32 create mode 100644 pyro/incompressible_viscous/problems/inputs.converge.64 create mode 100644 pyro/incompressible_viscous/problems/inputs.shear create mode 100644 pyro/incompressible_viscous/problems/plot_cavity.py create mode 100644 pyro/incompressible_viscous/problems/shear.py create mode 100644 pyro/incompressible_viscous/simulation.py create mode 100644 pyro/incompressible_viscous/tests/cavity_n64_Re400_0025.h5 create mode 100644 pyro/incompressible_viscous/tests/convergence_errors.py create mode 100644 pyro/incompressible_viscous/tests/convergence_errors.txt create mode 100644 pyro/incompressible_viscous/tests/convergence_errors_no_limiter.txt create mode 100644 pyro/incompressible_viscous/tests/convergence_errors_zero_viscosity.txt create mode 100644 pyro/incompressible_viscous/tests/convergence_plot.py diff --git a/.gitignore b/.gitignore index 8245ad3d3..3c78a9482 100755 --- a/.gitignore +++ b/.gitignore @@ -22,7 +22,10 @@ inputs.auto __pycache__/ +.DS_Store + pyro/_version.py pyro.egg-info/ +pyro_hydro.egg-info/ .eggs/ diff --git a/README.md b/README.md index 62c98332a..17813d7e7 100644 --- a/README.md +++ b/README.md @@ -157,6 +157,9 @@ pyro provides the following solvers (all in 2-d): projection method for the incompressible equations of hydrodynamics. + - `incompressible_viscous`: an extension of the incompressible solver + including a diffusion term for viscosity. + - `lm_atm`: a solver for the equations of low Mach number hydrodynamics for atmospheric flows. diff --git 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self.do_other_update_velocity(U_MAC, U_INT) - # we want u_MAC U_x + v_MAC U_y - advect_x = myg.scratch_array() - advect_y = myg.scratch_array() + else: + if self.verbose > 0: + print(" doing provisional update of u, v") - # u u_x + v u_y - advect_x.v()[:, :] = \ - 0.5*(u_MAC.v() + u_MAC.ip(1))*(u_xint.ip(1) - u_xint.v())/myg.dx + \ - 0.5*(v_MAC.v() + v_MAC.jp(1))*(u_yint.jp(1) - u_yint.v())/myg.dy + # compute (U.grad)U - # u v_x + v v_y - advect_y.v()[:, :] = \ - 0.5*(u_MAC.v() + u_MAC.ip(1))*(v_xint.ip(1) - v_xint.v())/myg.dx + \ - 0.5*(v_MAC.v() + v_MAC.jp(1))*(v_yint.jp(1) - v_yint.v())/myg.dy + # we want u_MAC U_x + v_MAC U_y + advect_x = myg.scratch_array() + advect_y = myg.scratch_array() - proj_type = self.rp.get_param("incompressible.proj_type") + # u u_x + v u_y + advect_x.v()[:, :] = \ + 0.5*(u_MAC.v() + u_MAC.ip(1))*(u_xint.ip(1) - u_xint.v())/myg.dx + \ + 0.5*(v_MAC.v() + v_MAC.jp(1))*(u_yint.jp(1) - u_yint.v())/myg.dy - if proj_type == 1: - u[:, :] -= (self.dt*advect_x[:, :] + self.dt*gradp_x[:, :]) - v[:, :] -= (self.dt*advect_y[:, :] + self.dt*gradp_y[:, :]) + # u v_x + v v_y + advect_y.v()[:, :] = \ + 0.5*(u_MAC.v() + u_MAC.ip(1))*(v_xint.ip(1) - v_xint.v())/myg.dx + \ + 0.5*(v_MAC.v() + v_MAC.jp(1))*(v_yint.jp(1) - v_yint.v())/myg.dy - elif proj_type == 2: - u[:, :] -= self.dt*advect_x[:, :] - v[:, :] -= self.dt*advect_y[:, :] + if proj_type == 1: + u[:, :] -= (self.dt*advect_x[:, :] + self.dt*gradp_x[:, :]) + v[:, :] -= (self.dt*advect_y[:, :] + self.dt*gradp_y[:, :]) + + elif proj_type == 2: + u[:, :] -= self.dt*advect_x[:, :] + v[:, :] -= self.dt*advect_y[:, :] self.cc_data.fill_BC("x-velocity") self.cc_data.fill_BC("y-velocity") @@ -323,10 +350,10 @@ def evolve(self): # create the multigrid object mg = MG.CellCenterMG2d(myg.nx, myg.ny, - xl_BC_type="periodic", - xr_BC_type="periodic", - yl_BC_type="periodic", - yr_BC_type="periodic", + xl_BC_type=self.cc_data.BCs["phi"].xlb, + xr_BC_type=self.cc_data.BCs["phi"].xrb, + yl_BC_type=self.cc_data.BCs["phi"].ylb, + yr_BC_type=self.cc_data.BCs["phi"].yrb, xmin=myg.xmin, xmax=myg.xmax, ymin=myg.ymin, ymax=myg.ymax, verbose=0) @@ -438,3 +465,21 @@ def dovis(self): plt.pause(0.001) plt.draw() + + def define_other_bc(self): + """ + Used to set up user-defined BC's (see e.g. incompressible_viscous) + """ + + def other_source_term(self): + """ + Add source terms (other than gradp) for getting interface state values, + in the x and y directions + """ + return None, None + + def do_other_update_velocity(self, U_MAC, U_INT): + """ + Change the method for updating the velocity from the projected velocity + and interface states (see e.g. incompressible_viscous) + """ diff --git a/pyro/incompressible_viscous/BC.py b/pyro/incompressible_viscous/BC.py new file mode 100644 index 000000000..763fea5df --- /dev/null +++ b/pyro/incompressible_viscous/BC.py @@ -0,0 +1,50 @@ +""" +Solver-specific boundary conditions. Here, in particular, we +implement a "moving-lid" option, i.e. fixed tangential velocity at a wall. +""" + +from pyro.util import msg + + +def user(bc_name, bc_edge, variable, ccdata): + """ + A moving lid boundary. This fixes the tangent velocity at the boundary + to 1, and the y-velocity to 0. + + Parameters + ---------- + bc_name : {'moving_lid'} + The descriptive name for the boundary condition -- this allows + for pyro to have multiple types of user-supplied boundary + conditions. For this module, it needs to be 'moving_lid'. + bc_edge : {'ylb', 'yrb', 'xlb', 'xrb} + The boundary to update: ylb = lower y; yrb = upper y. + xlb = left x; xrb = right x + ccdata : CellCenterData2d object + The data object + """ + + myg = ccdata.grid + + if bc_name == "moving_lid": + + if bc_edge == "yrb": + + if variable in ("x-velocity", "u"): + v = ccdata.get_var(variable) + for j in range(myg.jhi+1, myg.jhi+myg.ng+1): + v[:, j] = 1.0 # unit velocity + + elif variable in ("y-velocity", "v"): + v = ccdata.get_var(variable) + for j in range(myg.jhi+1, myg.jhi+myg.ng+1): + v[:, j] = 0.0 + + else: + raise NotImplementedError("variable not defined") + + else: + msg.fail("error: moving_lid BC only implemented for 'yrb' (top boundary)") + + else: + msg.fail(f"error: bc type {bc_name} not supported") diff --git a/pyro/incompressible_viscous/__init__.py b/pyro/incompressible_viscous/__init__.py new file mode 100644 index 000000000..eb5da9e49 --- /dev/null +++ b/pyro/incompressible_viscous/__init__.py @@ -0,0 +1,24 @@ +""" +The pyro solver for incompressible and viscous flow. This implements a +second-order approximate projection method. The general flow is: + +* create the limited slopes of u and v (in both directions) + +* get the advective velocities through a piecewise linear Godunov + method + +* enforce the divergence constraint on the velocities through a + projection (the MAC projection) + +* recompute the interface states using the new advective velocity + +* Solve for U in a (decoupled) parabolic solve including viscosity term + +* project the final velocity to enforce the divergence constraint. + +The projections are done using multigrid +""" + +__all__ = ["simulation"] + +from .simulation import Simulation diff --git a/pyro/incompressible_viscous/_defaults b/pyro/incompressible_viscous/_defaults new file mode 100644 index 000000000..261f5e5e4 --- /dev/null +++ b/pyro/incompressible_viscous/_defaults @@ -0,0 +1,13 @@ +[incompressible] +limiter = 2 ; limiter (0 = none, 1 = 2nd order, 2 = 4th order) +proj_type = 2 ; what are we projecting? 1 includes -Gp term in U* + +[incompressible_viscous] +viscosity = 0.1 ; kinematic viscosity of the fluid (units L^2/T) + +[driver] +cfl = 0.8 + +[particles] +do_particles = 0 +particle_generator = grid diff --git a/pyro/incompressible_viscous/problems/__init__.py b/pyro/incompressible_viscous/problems/__init__.py new file mode 100644 index 000000000..45467c7fa --- /dev/null +++ b/pyro/incompressible_viscous/problems/__init__.py @@ -0,0 +1 @@ +__all__ = ['cavity', 'shear', 'converge'] diff --git a/pyro/incompressible_viscous/problems/_cavity.defaults b/pyro/incompressible_viscous/problems/_cavity.defaults new file mode 100644 index 000000000..ea00c4ec1 --- /dev/null +++ b/pyro/incompressible_viscous/problems/_cavity.defaults @@ -0,0 +1 @@ +[cavity] \ No newline at end of file diff --git a/pyro/incompressible_viscous/problems/_converge.defaults b/pyro/incompressible_viscous/problems/_converge.defaults new file mode 100644 index 000000000..2ca31515e --- /dev/null +++ b/pyro/incompressible_viscous/problems/_converge.defaults @@ -0,0 +1 @@ +[converge] diff --git a/pyro/incompressible_viscous/problems/_shear.defaults b/pyro/incompressible_viscous/problems/_shear.defaults new file mode 100644 index 000000000..2e80b6c5f --- /dev/null +++ b/pyro/incompressible_viscous/problems/_shear.defaults @@ -0,0 +1,4 @@ +[shear] +rho_s = 42.0 ; shear layer width +delta_s = 0.05 ; perturbuation amplitude + diff --git a/pyro/incompressible_viscous/problems/cavity.py b/pyro/incompressible_viscous/problems/cavity.py new file mode 100644 index 000000000..e15197e6b --- /dev/null +++ b/pyro/incompressible_viscous/problems/cavity.py @@ -0,0 +1,42 @@ +r""" +Initialize the lid-driven cavity problem. Run on a unit square with the top wall +moving to the right with unit velocity, driving the flow. The other three walls +are no-slip boundary conditions. The initial velocity of the fluid is zero. + +Since the length and velocity scales are both 1, the Reynolds number is 1/viscosity. + +References: +https://doi.org/10.1007/978-3-319-91494-7_8 +https://www.fluid.tuwien.ac.at/HendrikKuhlmann?action=AttachFile&do=get&target=LidDrivenCavity.pdf +""" + +from pyro.mesh import patch +from pyro.util import msg + + +def init_data(my_data, rp): + """ initialize the lid-driven cavity """ + del rp # this problem doesn't use runtime params + + msg.bold("initializing the lid-driven cavity problem...") + + # make sure that we are passed a valid patch object + if not isinstance(my_data, patch.CellCenterData2d): + print(my_data.__class__) + msg.fail("ERROR: patch invalid in cavity.py") + + myg = my_data.grid + + if (myg.xmin != 0 or myg.xmax != 1 or + myg.ymin != 0 or myg.ymax != 1): + msg.fail("ERROR: domain should be a unit square") + + # get the velocities and set them to zero + u = my_data.get_var("x-velocity") + v = my_data.get_var("y-velocity") + u[:, :] = 0 + v[:, :] = 0 + + +def finalize(): + """ print out any information to the user at the end of the run """ diff --git a/pyro/incompressible_viscous/problems/converge.py b/pyro/incompressible_viscous/problems/converge.py new file mode 100644 index 000000000..ee2139d7b --- /dev/null +++ b/pyro/incompressible_viscous/problems/converge.py @@ -0,0 +1,67 @@ +r""" +Initialize a smooth incompressible+viscous convergence test. Here, the +velocities are initialized as + +.. math:: + + u(x,y) = 1 - 2 \cos(2 \pi x) \sin(2 \pi y) + + v(x,y) = 1 + 2 \sin(2 \pi x) \cos(2 \pi y) + +and the exact solution at some later time t, for some viscosity nu, is + +.. math:: + + u(x,y,t) = 1 - 2 \cos(2 \pi (x - t)) \sin(2 \pi (y - t)) e^{-8 \pi^2 \nu t} + + v(x,y,t) = 1 + 2 \sin(2 \pi (x - t)) \cos(2 \pi (y - t)) e^{-8 \pi^2 \nu t} + + p(x,y,t) = - (\cos(4 \pi (x - t)) + \cos(4 \pi (y - t))) e^{-16 \pi^2 \nu t} + +The numerical solution can be compared to the exact solution to +measure the convergence rate of the algorithm. +""" + + +import math + +import numpy as np + +from pyro.mesh import patch +from pyro.util import msg + + +def init_data(my_data, rp): + """ initialize the incompressible viscous converge problem """ + del rp # this problem doesn't use runtime params + + msg.bold("initializing the incompressible viscous converge problem...") + + # make sure that we are passed a valid patch object + if not isinstance(my_data, patch.CellCenterData2d): + print(my_data.__class__) + msg.fail("ERROR: patch invalid in converge.py") + + # get the velocities + u = my_data.get_var("x-velocity") + v = my_data.get_var("y-velocity") + + myg = my_data.grid + + if (myg.xmin != 0 or myg.xmax != 1 or + myg.ymin != 0 or myg.ymax != 1): + msg.fail("ERROR: domain should be a unit square") + + u[:, :] = 1.0 - 2.0*np.cos(2.0*math.pi*myg.x2d)*np.sin(2.0*math.pi*myg.y2d) + v[:, :] = 1.0 + 2.0*np.sin(2.0*math.pi*myg.x2d)*np.cos(2.0*math.pi*myg.y2d) + + +def finalize(): + """ print out any information to the user at the end of the run """ + + ostr = """ + Comparisons to the analytic solution can be done using + analysis/incomp_viscous_converge_error.py + """ + + print(ostr) diff --git a/pyro/incompressible_viscous/problems/inputs.cavity b/pyro/incompressible_viscous/problems/inputs.cavity new file mode 100644 index 000000000..2d438af3c --- /dev/null +++ b/pyro/incompressible_viscous/problems/inputs.cavity @@ -0,0 +1,31 @@ +# simple inputs files for the unsplit CTU hydro scheme + +[driver] +max_steps = 25 +tmax = 5.0 +cfl = 0.8 + + +[incompressible_viscous] +viscosity = 0.0025 + + +[io] +basename = cavity_n64_Re400_ +dt_out = 1 +n_out = 25 + + +[mesh] +nx = 64 +ny = 64 +xmax = 1.0 +ymax = 1.0 + +xlboundary = dirichlet +xrboundary = dirichlet +ylboundary = dirichlet +yrboundary = moving_lid + + +[cavity] diff --git a/pyro/incompressible_viscous/problems/inputs.converge.128 b/pyro/incompressible_viscous/problems/inputs.converge.128 new file mode 100644 index 000000000..9a1b3c4b1 --- /dev/null +++ b/pyro/incompressible_viscous/problems/inputs.converge.128 @@ -0,0 +1,36 @@ +# simple inputs files for the incompressible convergence test + +[driver] +max_steps = 1000 +tmax = 0.1 +cfl = 0.5 +init_tstep_factor = 1.0 +fix_dt = 1.25e-3 + + +[incompressible_viscous] +viscosity = 0.1 + + +[io] +basename = converge_viscous_128_ +dt_out = 0.1 + + +[mesh] +nx = 128 +ny = 128 +xmax = 1.0 +ymax = 1.0 + +xlboundary = periodic +xrboundary = periodic + +ylboundary = periodic +yrboundary = periodic + + +[converge] + + + diff --git a/pyro/incompressible_viscous/problems/inputs.converge.32 b/pyro/incompressible_viscous/problems/inputs.converge.32 new file mode 100644 index 000000000..4819149b3 --- /dev/null +++ b/pyro/incompressible_viscous/problems/inputs.converge.32 @@ -0,0 +1,36 @@ +# simple inputs files for the incompressible convergence test + +[driver] +max_steps = 1000 +tmax = 0.1 +cfl = 0.5 +init_tstep_factor = 1.0 +fix_dt = 5.e-3 + + +[incompressible_viscous] +viscosity = 0.1 + + +[io] +basename = converge_viscous_32_ +dt_out = 0.1 + + +[mesh] +nx = 32 +ny = 32 +xmax = 1.0 +ymax = 1.0 + +xlboundary = periodic +xrboundary = periodic + +ylboundary = periodic +yrboundary = periodic + + +[converge] + + + diff --git a/pyro/incompressible_viscous/problems/inputs.converge.64 b/pyro/incompressible_viscous/problems/inputs.converge.64 new file mode 100644 index 000000000..8c60d0e7b --- /dev/null +++ b/pyro/incompressible_viscous/problems/inputs.converge.64 @@ -0,0 +1,36 @@ +# simple inputs files for the incompressible convergence test + +[driver] +max_steps = 1000 +tmax = 0.1 +cfl = 0.5 +init_tstep_factor = 1.0 +fix_dt = 2.5e-3 + + +[incompressible_viscous] +viscosity = 0.1 + + +[io] +basename = converge_viscous_64_ +dt_out = 0.1 + + +[mesh] +nx = 64 +ny = 64 +xmax = 1.0 +ymax = 1.0 + +xlboundary = periodic +xrboundary = periodic + +ylboundary = periodic +yrboundary = periodic + + +[converge] + + + diff --git a/pyro/incompressible_viscous/problems/inputs.shear b/pyro/incompressible_viscous/problems/inputs.shear new file mode 100644 index 000000000..e85064156 --- /dev/null +++ b/pyro/incompressible_viscous/problems/inputs.shear @@ -0,0 +1,35 @@ +# simple inputs files for the unsplit CTU hydro scheme + +[driver] +max_steps = 2000 +tmax = 1.0 +cfl = 0.8 + + +[incompressible_viscous] +viscosity = 0.001 + + +[io] +basename = shear_viscous_128_ +n_out = 1 + + +[mesh] +nx = 128 +ny = 128 +xmax = 1.0 +ymax = 1.0 + +xlboundary = periodic +xrboundary = periodic + +ylboundary = periodic +yrboundary = periodic + + +[shear] +rho_s = 42.0 +delta_s = 0.05 + + diff --git a/pyro/incompressible_viscous/problems/plot_cavity.py b/pyro/incompressible_viscous/problems/plot_cavity.py new file mode 100644 index 000000000..c109f0162 --- /dev/null +++ b/pyro/incompressible_viscous/problems/plot_cavity.py @@ -0,0 +1,82 @@ +#!/usr/bin/env python3 + +import argparse + +import matplotlib as mpl +import matplotlib.pyplot as plt +import numpy as np + +import pyro.util.io_pyro as io + +mpl.rcParams["text.usetex"] = True +mpl.rcParams['mathtext.fontset'] = 'cm' +mpl.rcParams['mathtext.rm'] = 'serif' + +# font sizes +mpl.rcParams['font.size'] = 12 +mpl.rcParams['legend.fontsize'] = 'large' +mpl.rcParams['figure.titlesize'] = 'medium' + + +def makeplot(plotfile_name, outfile, Reynolds, streamline_density): + """ plot the velocity magnitude and streamlines """ + + sim = io.read(plotfile_name) + myg = sim.cc_data.grid + x = myg.x[myg.ilo:myg.ihi+1] + y = myg.y[myg.jlo:myg.jhi+1] + u = sim.cc_data.get_var("x-velocity") + v = sim.cc_data.get_var("y-velocity") + magvel = np.sqrt(u**2+v**2) + + _, ax = plt.subplots(1, 1) + ax.set_aspect('equal') + + img = ax.contourf(x, y, np.transpose(magvel.v()), 30, cmap="magma") + ax.streamplot(x, y, np.transpose(u.v()), np.transpose(v.v()), broken_streamlines=False, + linewidth=0.5, arrowstyle="-", density=streamline_density, color='w') + + cbar = plt.colorbar(img, ax=ax) + cbar.ax.tick_params(labelsize=8) + cbar.ax.get_yaxis().labelpad = 15 + cbar.ax.set_ylabel("velocity magnitude", rotation=270) + plt.xlabel("x") + plt.ylabel("y") + + title = "" + if Reynolds is not None: + title += f"Re = {Reynolds}" + + # The characteristic timescale tau is the length of the box divided by the lid velocity. + # For the default parameters, tau=1 + # title += rf", $t/\tau = $ {sim.cc_data.t:.1f}" + plt.title(title) + + if outfile.endswith(".pdf"): + plt.savefig(outfile, bbox_inches="tight") + else: + plt.savefig(outfile, bbox_inches="tight", dpi=500) + plt.show() + + +def get_args(): + + parser = argparse.ArgumentParser() + + parser.add_argument("-o", type=str, default="plot.png", + metavar="plot.png", help="output file name") + parser.add_argument("-Re", type=int, + metavar="Reynolds", help="Reynolds number (1/viscosity)") + parser.add_argument("-d", type=float, default=0.25, + metavar="density", help="density of streamlines (0 to 1)") + parser.add_argument("plotfile", type=str, nargs=1, + help="the plotfile you wish to plot") + + return parser.parse_args() + + +if __name__ == "__main__": + + args = get_args() + + makeplot(args.plotfile[0], args.o, args.Re, args.d) diff --git a/pyro/incompressible_viscous/problems/shear.py b/pyro/incompressible_viscous/problems/shear.py new file mode 100644 index 000000000..64009a1bd --- /dev/null +++ b/pyro/incompressible_viscous/problems/shear.py @@ -0,0 +1,67 @@ +r""" +Initialize the doubly periodic shear layer (see, for example, Martin +and Colella, 2000, JCP, 163, 271). This is run in a unit square +domain, with periodic boundary conditions on all sides. Here, the +initial velocity is:: + + / tanh(rho_s (y-0.25)) if y <= 0.5 + u(x,y,t=0) = < + \ tanh(rho_s (0.75-y)) if y > 0.5 + + v(x,y,t=0) = delta_s sin(2 pi x) + + +""" + + +import math + +import numpy as np + +from pyro.mesh import patch +from pyro.util import msg + + +def init_data(my_data, rp): + """ initialize the incompressible shear problem """ + + msg.bold("initializing the incompressible shear problem...") + + # make sure that we are passed a valid patch object + if not isinstance(my_data, patch.CellCenterData2d): + print(my_data.__class__) + msg.fail("ERROR: patch invalid in shear.py") + + # get the necessary runtime parameters + rho_s = rp.get_param("shear.rho_s") + delta_s = rp.get_param("shear.delta_s") + + # get the velocities + u = my_data.get_var("x-velocity") + v = my_data.get_var("y-velocity") + + myg = my_data.grid + + if (myg.xmin != 0 or myg.xmax != 1 or + myg.ymin != 0 or myg.ymax != 1): + msg.fail("ERROR: domain should be a unit square") + + y_half = 0.5*(myg.ymin + myg.ymax) + + print('y_half = ', y_half) + print('delta_s = ', delta_s) + print('rho_s = ', rho_s) + + idx = myg.y2d <= y_half + u[idx] = np.tanh(rho_s*(myg.y2d[idx] - 0.25)) + + idx = myg.y2d > y_half + u[idx] = np.tanh(rho_s*(0.75 - myg.y2d[idx])) + + v[:, :] = delta_s*np.sin(2.0*math.pi*myg.x2d) + + print("extrema: ", u.min(), u.max()) + + +def finalize(): + """ print out any information to the user at the end of the run """ diff --git a/pyro/incompressible_viscous/simulation.py b/pyro/incompressible_viscous/simulation.py new file mode 100644 index 000000000..ee02fcbca --- /dev/null +++ b/pyro/incompressible_viscous/simulation.py @@ -0,0 +1,190 @@ +from pyro import incompressible +from pyro.incompressible_viscous import BC +from pyro.mesh import boundary as bnd +from pyro.multigrid import MG + + +class Simulation(incompressible.Simulation): + + def initialize(self): # pylint: disable=arguments-differ + """ + Initialization of the data is the same as the incompressible + solver, but we define user BC, and provide the viscosity + as an auxiliary variable. + """ + nu = self.rp.get_param("incompressible_viscous.viscosity") + + super().initialize(other_bc=True, + aux_vars=(("viscosity", nu),)) + + def define_other_bc(self): + bnd.define_bc("moving_lid", BC.user, is_solid=False) + + def evolve(self): # pylint: disable=arguments-differ + """ + Solve is all the same steps as the incompressible solver, but + including a source term for the viscosity in the interface + prediction, and changing the velocity update method to a double + parabolic solve. + """ + super().evolve(other_update_velocity=True, other_source_term=True) + + def other_source_term(self): + """ + This is the viscous term nu L U + """ + u = self.cc_data.get_var("x-velocity") + v = self.cc_data.get_var("y-velocity") + myg = self.cc_data.grid + nu = self.rp.get_param("incompressible_viscous.viscosity") + + source_x = myg.scratch_array() + source_x.v()[:, :] = nu * ((u.ip(1) + u.ip(-1) - 2.0*u.v())/myg.dx**2 + + (u.jp(1) + u.jp(-1) - 2.0*u.v())/myg.dy**2) + + source_y = myg.scratch_array() + source_y.v()[:, :] = nu * ((v.ip(1) + v.ip(-1) - 2.0*v.v())/myg.dx**2 + + (v.jp(1) + v.jp(-1) - 2.0*v.v())/myg.dy**2) + + return source_x, source_y + + def do_other_update_velocity(self, U_MAC, U_INT): + """ + Solve for U in a (decoupled) parabolic solve including viscosity term + """ + + if self.verbose > 0: + print(" doing parabolic solve for u, v") + + # Get variables + u = self.cc_data.get_var("x-velocity") + v = self.cc_data.get_var("y-velocity") + gradp_x = self.cc_data.get_var("gradp_x") + gradp_y = self.cc_data.get_var("gradp_y") + myg = self.cc_data.grid + nu = self.rp.get_param("incompressible_viscous.viscosity") + proj_type = self.rp.get_param("incompressible.proj_type") + + # Get MAC and interface velocities from function args + u_MAC, v_MAC = U_MAC + u_xint, u_yint, v_xint, v_yint = U_INT + + # compute (U.grad)U terms + + # we want u_MAC U_x + v_MAC U_y + advect_x = myg.scratch_array() + advect_y = myg.scratch_array() + + # u u_x + v u_y + advect_x.v()[:, :] = \ + 0.5*(u_MAC.v() + u_MAC.ip(1))*(u_xint.ip(1) - u_xint.v())/myg.dx + \ + 0.5*(v_MAC.v() + v_MAC.jp(1))*(u_yint.jp(1) - u_yint.v())/myg.dy + + # u v_x + v v_y + advect_y.v()[:, :] = \ + 0.5*(u_MAC.v() + u_MAC.ip(1))*(v_xint.ip(1) - v_xint.v())/myg.dx + \ + 0.5*(v_MAC.v() + v_MAC.jp(1))*(v_yint.jp(1) - v_yint.v())/myg.dy + + # setup the MG object -- we want to solve a Helmholtz equation + # equation of the form: + # (alpha - beta L) U = f + # + # with alpha = 1 + # beta = (dt/2) nu + # f = U + dt * (0.5*nu L U - (U.grad)U - grad p) + # + # (one such equation for each velocity component) + # + # this is the form that arises with a Crank-Nicolson discretization + # of the incompressible momentum equation + + # Solve for x-velocity + + mg = MG.CellCenterMG2d(myg.nx, myg.ny, + xmin=myg.xmin, xmax=myg.xmax, + ymin=myg.ymin, ymax=myg.ymax, + xl_BC_type=self.cc_data.BCs["x-velocity"].xlb, + xr_BC_type=self.cc_data.BCs["x-velocity"].xrb, + yl_BC_type=self.cc_data.BCs["x-velocity"].ylb, + yr_BC_type=self.cc_data.BCs["x-velocity"].yrb, + alpha=1.0, beta=0.5*self.dt*nu, + verbose=0) + + # form the RHS: f = u + (dt/2) nu L u (where L is the Laplacian) + f = mg.soln_grid.scratch_array() + f.v()[:, :] = u.v() + 0.5*self.dt * nu * ( + (u.ip(1) + u.ip(-1) - 2.0*u.v())/myg.dx**2 + + (u.jp(1) + u.jp(-1) - 2.0*u.v())/myg.dy**2) # this is the diffusion part + + # f.v()[:, :] = u_MAC.v() + 0.5*self.dt * nu * ( + # (u_MAC.ip(1) + u_MAC.ip(-1) - 2.0*u_MAC.v())/myg.dx**2 + + # (u_MAC.jp(1) + u_MAC.jp(-1) - 2.0*u_MAC.v())/myg.dy**2) # this is the diffusion part + + if proj_type == 1: + f.v()[:, :] -= self.dt * (advect_x.v() + gradp_x.v()) # advection + pressure + elif proj_type == 2: + f.v()[:, :] -= self.dt * advect_x.v() # advection only + + mg.init_RHS(f) + + # use the old u as our initial guess + uGuess = mg.soln_grid.scratch_array() + uGuess.v(buf=1)[:, :] = u.v(buf=1) + mg.init_solution(uGuess) + + # solve + mg.solve(rtol=1.e-12) + + # store the solution + u.v()[:, :] = mg.get_solution().v() + + # Solve for y-velocity + + mg = MG.CellCenterMG2d(myg.nx, myg.ny, + xmin=myg.xmin, xmax=myg.xmax, + ymin=myg.ymin, ymax=myg.ymax, + xl_BC_type=self.cc_data.BCs["y-velocity"].xlb, + xr_BC_type=self.cc_data.BCs["y-velocity"].xrb, + yl_BC_type=self.cc_data.BCs["y-velocity"].ylb, + yr_BC_type=self.cc_data.BCs["y-velocity"].yrb, + alpha=1.0, beta=0.5*self.dt*nu, + verbose=0) + + # form the RHS: f = v + (dt/2) nu L v (where L is the Laplacian) + f = mg.soln_grid.scratch_array() + f.v()[:, :] = v.v() + 0.5*self.dt * nu * ( + (v.ip(1) + v.ip(-1) - 2.0*v.v())/myg.dx**2 + + (v.jp(1) + v.jp(-1) - 2.0*v.v())/myg.dy**2) + + # f.v()[:, :] = v_MAC.v() + 0.5*self.dt * nu * ( + # (v_MAC.ip(1) + v_MAC.ip(-1) - 2.0*v_MAC.v())/myg.dx**2 + + # (v_MAC.jp(1) + v_MAC.jp(-1) - 2.0*v_MAC.v())/myg.dy**2) + + if proj_type == 1: + f.v()[:, :] -= self.dt * (advect_y.v() + gradp_y.v()) # advection + pressure + elif proj_type == 2: + f.v()[:, :] -= self.dt * advect_y.v() # advection only + + mg.init_RHS(f) + + # use the old v as our initial guess + uGuess = mg.soln_grid.scratch_array() + uGuess.v(buf=1)[:, :] = v.v(buf=1) + mg.init_solution(uGuess) + + # solve + mg.solve(rtol=1.e-12) + + # store the solution + v.v()[:, :] = mg.get_solution().v() + + def write_extras(self, f): + """ + Output simulation-specific data to the h5py file f + """ + + # make note of the custom BC + gb = f.create_group("BC") + + # the value here is the value of "is_solid" + gb.create_dataset("moving_lid", data=False) diff --git a/pyro/incompressible_viscous/tests/cavity_n64_Re400_0025.h5 b/pyro/incompressible_viscous/tests/cavity_n64_Re400_0025.h5 new file mode 100644 index 0000000000000000000000000000000000000000..ed8bce1565fed60746b9137bfa4131dc4227a21e GIT binary patch literal 219089 zcmeFYbzGI(w>Juiiim-fNhlzSAfbRLF6k1aL%JIl-Q6YKAt6#CC?TTqr33^)!az|$ 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b/pyro/incompressible_viscous/tests/convergence_errors.py @@ -0,0 +1,37 @@ +# This should be run from /pyro (where the output files are located) +import glob +import sys + +from pyro.analysis.incomp_viscous_converge_error import get_errors + + +def create_file(filename="convergence_errors.txt"): + + # Parse all converge*.h5 outputs + # store the last file at each resolution + fnames = glob.glob("converge_viscous*.h5") + res = {f.split("_")[2] for f in fnames} + res = list(res) + res.sort(key=int) + + simfiles = [] + for r in res: + fnames = glob.glob(f"converge_viscous_{r}_*.h5") + last = max(int(f.split("_")[-1].split(".")[0]) for f in fnames) + simfiles.append(f"converge_viscous_{r}_{last:04d}.h5") + + # Create the file + with open("incompressible_viscous/tests/" + filename, "w") as f: + f.write("# convergence of incompressible viscous converge problem\n") + f.write("# (convergence measured with analysis/incomp_viscous_converge_error.py)\n") + f.write("#\n") + for r, file in zip(res, simfiles): + errors = get_errors(file) + f.write(f"{r.rjust(3)} {errors[0]:.14f} {errors[1]:.14f}\n") + + +if __name__ == "__main__": + if len(sys.argv) == 2: + create_file(sys.argv[1]) + else: + create_file() diff --git a/pyro/incompressible_viscous/tests/convergence_errors.txt b/pyro/incompressible_viscous/tests/convergence_errors.txt new file mode 100644 index 000000000..162734cc3 --- /dev/null +++ b/pyro/incompressible_viscous/tests/convergence_errors.txt @@ -0,0 +1,6 @@ +# convergence of incompressible viscous converge problem +# (convergence measured with analysis/incomp_viscous_converge_error.py) +# + 32 0.00551576423899 0.00552893258797 + 64 0.00243829830121 0.00243861957534 +128 0.00112687217317 0.00112695662547 diff --git a/pyro/incompressible_viscous/tests/convergence_errors_no_limiter.txt b/pyro/incompressible_viscous/tests/convergence_errors_no_limiter.txt new file mode 100644 index 000000000..edd47a4f7 --- /dev/null +++ b/pyro/incompressible_viscous/tests/convergence_errors_no_limiter.txt @@ -0,0 +1,6 @@ +# convergence of incompressible viscous converge problem +# (convergence measured with analysis/incomp_viscous_converge_error.py) +# + 32 0.00524720002483 0.00526026574257 + 64 0.00240838322318 0.00240868549772 +128 0.00112377672989 0.00112384687025 diff --git a/pyro/incompressible_viscous/tests/convergence_errors_zero_viscosity.txt b/pyro/incompressible_viscous/tests/convergence_errors_zero_viscosity.txt new file mode 100644 index 000000000..715467799 --- /dev/null +++ b/pyro/incompressible_viscous/tests/convergence_errors_zero_viscosity.txt @@ -0,0 +1,6 @@ +# convergence of incompressible viscous converge problem +# (convergence measured with analysis/incomp_viscous_converge_error.py) +# + 32 0.02207392410018 0.02207392410018 + 64 0.00682161894998 0.00682161894998 +128 0.00214081341364 0.00214081341364 diff --git a/pyro/incompressible_viscous/tests/convergence_plot.py b/pyro/incompressible_viscous/tests/convergence_plot.py new file mode 100644 index 000000000..7a9af4986 --- /dev/null +++ b/pyro/incompressible_viscous/tests/convergence_plot.py @@ -0,0 +1,52 @@ +import os + +import matplotlib.pyplot as plt +import numpy as np + + +def plot_convergence(): + + ax = plt.subplot(111) + ax.set_xscale('log') + ax.set_yscale('log') + + files = ["incompressible_viscous/tests/convergence_errors.txt", + "incompressible_viscous/tests/convergence_errors_no_limiter.txt"] + + if not os.path.exists(files[0]): + print("Could not find convergence_errors.txt") + else: + data = np.loadtxt(files[0]) + nx = data[:, 0] + errlim = data[:, 1] + + plt.scatter(nx, errlim, marker="x", color="r", label="limiting") + plt.plot(nx, errlim[0]*(nx[0]/nx)**2, "--", color="k") + + if not os.path.exists(files[1]): + print("Could not find convergence_errors_no_limiter.txt") + else: + data = np.loadtxt(files[1]) + nx = data[:, 0] + errlim = data[:, 1] + + plt.scatter(nx, errlim, marker="x", color="b", label="no limiting") + + plt.xlabel("number of zones") + plt.ylabel("L2 norm of abs error") + plt.legend(frameon=False) + + plt.title(r"convergence for incompressible viscous solver", fontsize=11) + + f = plt.gcf() + f.set_size_inches(5.0, 5.0) + + plt.xlim(16, 256) + plt.ylim(2.e-4, 2.e-2) + + plt.savefig("incomp_viscous_converge.png", bbox_inches="tight") + plt.savefig("incomp_viscous_converge.eps", bbox_inches="tight") + + +if __name__ == "__main__": + plot_convergence() diff --git a/pyro/pyro_sim.py b/pyro/pyro_sim.py index 6384cfd68..4d5ff8d2b 100755 --- a/pyro/pyro_sim.py +++ b/pyro/pyro_sim.py @@ -25,6 +25,7 @@ "compressible_sr", "diffusion", "incompressible", + "incompressible_viscous", "lm_atm", "swe"] diff --git a/pyro/test.py b/pyro/test.py index 402c9cbb6..b51f1421a 100755 --- a/pyro/test.py +++ b/pyro/test.py @@ -109,6 +109,7 @@ def do_tests(out_file, tests.append(PyroTest("diffusion", "gaussian", "inputs.gaussian", opts)) tests.append(PyroTest("incompressible", "shear", "inputs.shear", opts)) + tests.append(PyroTest("incompressible_viscous", "cavity", "inputs.cavity", opts)) tests.append(PyroTest("lm_atm", "bubble", "inputs.bubble", opts)) tests.append(PyroTest("swe", "dam", "inputs.dam.x", opts))

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