ns2div

ns2div is a GPU accelerated Python solver for Navier-Stokes equations with variable density on structurely meshed rectangular domains. Please refer to the following paper for details:

Monica Dessole, Fabio Marcuzzi "Fully iterative ILU preconditioning of the unsteady Navier–Stokes equations for GPGPU", Computers & Mathematics with Applications Volume 77, Issue 4, 15 February 2019, Pages 907-92.

The numerical scheme implemented is based on the NS2DDV Matlab toolbox. Strang splitting is used to decouple the transpost problem concerning the density the from the Navier-Stokes problem, describing the velocity and the pressure of the fluid. The former is treated with a Finite Volume scheme, in the latter a second-order Finite Element projection scheme is used to decouple the pressure and the components of the velocity field, each of them is obtained by solving on a GPU a sparse linear system with GMRES with an LU type preconditioner which is updated with the Simplified ITALU procedure.

Running ns2div

Clean existing shared library

rm *.so

In order to run a test one shoud execute the file test_profile.py with the inputs nbseg_x (number of mesh intervals in the x-direction), nbseg_y (number of mesh intervals in the y-direction), BENCHMARK (EXAC, RTIN or DROP). For example

python test_profile.py 8 8 EXAC

run the exact test case on a 8x8 structured mesh.

In order to compute the order of convergence one can run

python test_convergence.py 

Manual setup

One can choose a particular configuration for the execution by changing the values of the following parameters in the file manual_setup.py:

• test_output = 0 (1 enable output data storage at each time step), 0 (output data storage disabled)

• ns.test_plot = 0 (1 enable plot making in RTIN or DROP test cases), 0 (plots disabled)

• ns.prec = 0 (no preconditioner), 1 (diagonal preconditioner), 2 (ILU(0) preconditioner)

• iterLU = 1 (enable ILU(0) with ITALU updates), 0 (ITALU disabled)

  • ns.initialize_LU = 0 (0 initialize L,U con ILU(0)), 1 (inizialize L,U con tril,triu)
  • ns.iters = 1 (number of ITALU iterations)
  • ns.ITALU_update_param = k (if k > 1, the ITALU procedure is applied every k iterations)

  Parameters for L/U triangular linear systems solution in the application of the preconditioner

  • ns.LU_scalar_jacobi = 0 (direct solver), 1 (Jacobi iterative solver)
  • ns.LU_block_jacobi = 0 (direct solver), 1 (Block Jacobi iterative solver)
  • ns.LUit_iters = 3 (number of Jacobi iterations)
  • ns.approx_diag_LU = 0 (band approximation disabled), 1 (enable approximation of L/U by a band matrix)
  • ns.diag = 3 (desired bandwidth)
  • ns.cutDAG_LU = 0 (DAG cutting disabled), 1 (enable DAG cutting)
  • ns.cut = 1/2 (percentage between 0 and 1 of levels to be deleted from the DAG of L/U)

Dependencies

• Python 3
• Numpy
• Scipy
• Pycuda
• Cuda 9