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DEMO_mhdm.m
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%
% Turbmat - a Matlab library for the JHU Turbulence Database Cluster
%
% Sample code, part of Turbmat
%
%
% Written by:
%
% Perry Johnson
% The Johns Hopkins University
% Department of Mechanical Engineering
%
% 2017: Modified by Zhao Wu and Rohit Ravoori, adding getInvariant
% 2019: Modified by Zhao Wu for getThreshold function
%
% This file is part of Turbmat.
%
% Turbmat is free software: you can redistribute it and/or modify it under
% the terms of the GNU General Public License as published by the Free
% Software Foundation, either version 3 of the License, or (at your option)
% any later version.
%
% Turbmat is distributed in the hope that it will be useful, but WITHOUT
% ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
% FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
% more details.
%
% You should have received a copy of the GNU General Public License along
% with Turbmat. If not, see <http://www.gnu.org/licenses/>.
%
clear all;
close all;
authkey = 'edu.jhu.pha.turbulence.testing-201406';
dataset = 'mhd1024';
% ---- Temporal Interpolation Options ----
NoTInt = 'None' ; % No temporal interpolation
PCHIPInt = 'PCHIP'; % Piecewise cubic Hermit interpolation in time
% ---- Spatial Interpolation Flags for getVelocity & getVelocityAndPressure ----
NoSInt = 'None'; % No spatial interpolation
Lag4 = 'Lag4'; % 4th order Lagrangian interpolation in space
Lag6 = 'Lag6'; % 6th order Lagrangian interpolation in space
Lag8 = 'Lag8'; % 8th order Lagrangian interpolation in space
% ---- Spatial Differentiation & Interpolation Flags for getVelocityGradient & getPressureGradient ----
FD4NoInt = 'None_Fd4' ; % 4th order finite differential scheme for grid values, no spatial interpolation
FD6NoInt = 'None_Fd6' ; % 6th order finite differential scheme for grid values, no spatial interpolation
FD8NoInt = 'None_Fd8' ; % 8th order finite differential scheme for grid values, no spatial interpolation
FD4Lag4 = 'Fd4Lag4' ; % 4th order finite differential scheme for grid values, 4th order Lagrangian interpolation in space
% ---- Spline interpolation and differentiation Flags for getVelocity,
% getPressure, getVelocityGradient, getPressureGradient,
% getVelocityHessian, getPressureHessian
M1Q4 = 'M1Q4'; % Splines with smoothness 1 (3rd order) over 4 data points. Not applicable for Hessian.
M2Q8 = 'M2Q8'; % Splines with smoothness 2 (5th order) over 8 data points.
M2Q14 = 'M2Q14'; % Splines with smoothness 2 (5th order) over 14 data points.
% Set time step to sample
time = 0.364;
% getPosition integration settings
startTime=0.364;
endTime=0.414;
lagDt=0.005;
npoints = 10;
% for box filtering
field = 'velocity';
scalar_fields = 'pp'; % two scalar fields ("p" and "p")
vector_scalar_fields = 'up'; % a vector and a scalar field ("u" and "p")
vector_fields = 'ub'; % two vector fields ("u" and "b")
dx = 2. * pi / 1024;
filterwidth = 7. * dx;
spacing = 4. * dx;
% for thresholding
threshold_field = 'vorticity';
threshold = 65.0;
x_start = int32(1);
y_start = int32(1);
z_start = int32(1);
x_end = int32(16);
y_end = int32(16);
z_end = int32(16);
points = zeros(3,npoints);
result1 = zeros(npoints);
result2 = zeros(2,npoints);
result3 = zeros(3,npoints);
result4 = zeros(4,npoints);
result6 = zeros(6,npoints);
result9 = zeros(9,npoints);
result18 = zeros(18,npoints);
% Set spatial locations to sample
for p = 1:npoints
points(1,p) = 0.20 * p;
points(2,p) = 0.50 * p;
points(3,p) = 0.15 * p;
end
fprintf('\nCoordinates of 10 points where variables are requested:\n');
for p = 1:npoints
fprintf(1,'%3i: %13.6e, %13.6e, %13.6e\n', p, points(1,p), points(2,p), points(3,p));
end
fprintf('\nRequesting velocity at %i points...\n',npoints);
result3 = getVelocity (authkey, dataset, time, Lag6, NoTInt, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: %13.6e, %13.6e, %13.6e\n', p, result3(1,p), result3(2,p), result3(3,p));
end
fprintf('\nRequesting forcing at %i points...\n',npoints);
result3 = getForce (authkey, dataset, time, Lag6, NoTInt, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: %13.6e, %13.6e, %13.6e\n', p, result3(1,p), result3(2,p), result3(3,p));
end
fprintf('\nRequesting velocity and pressure at %i points...\n',npoints);
result4 = getVelocityAndPressure (authkey, dataset, time, Lag6, NoTInt, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: %13.6e, %13.6e, %13.6e, %13.6e\n', p, result4(1,p), result4(2,p), result4(3,p), result4(4,p));
end
fprintf('\nRequesting velocity gradient at %i points...\n',npoints);
result9 = getVelocityGradient (authkey, dataset, time, FD4Lag4, NoTInt, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: duxdx=%13.6e, duxdy=%13.6e, duxdz=%13.6e, ', p, result9(1,p), result9(2,p), result9(3,p));
fprintf(1,'duydx=%13.6e, duydy=%13.6e, duydz=%13.6e, ', result9(4,p), result9(5,p), result9(6,p));
fprintf(1,'duzdx=%13.6e, duzdy=%13.6e, duzdz=%13.6e\n', result9(7,p), result9(8,p), result9(9,p));
end
fprintf('\nRequesting velocity hessian at %i points...\n',npoints);
result18 = getVelocityHessian (authkey, dataset, time, FD4Lag4, NoTInt, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: d2uxdxdx=%13.6e, d2uxdxdy=%13.6e, d2uxdxdz=%13.6e, ', p, result18(1,p), result18(2,p), result18(3,p));
fprintf(1,'d2uxdydy=%13.6e, d2uxdydz=%13.6e, d2uxdzdz=%13.6e, ', result18(4,p), result18(5,p), result18(6,p));
fprintf(1,'d2uydxdx=%13.6e, d2uydxdy=%13.6e, d2uydxdz=%13.6e, ', result18(7,p), result18(8,p), result18(9,p));
fprintf(1,'d2uydydy=%13.6e, d2uydydz=%13.6e, d2uydzdz=%13.6e, ', result18(10,p), result18(11,p), result18(12,p));
fprintf(1,'d2uzdxdx=%13.6e, d2uzdxdy=%13.6e, d2uzdxdz=%13.6e, ', result18(13,p), result18(14,p), result18(15,p));
fprintf(1,'d2uzdydy=%13.6e, d2uzdydz=%13.6e, d2uzdzdz=%13.6e\n', result18(16,p), result18(17,p), result18(18,p));
end
fprintf('\nRequesting velocity laplacian at %i points...\n',npoints);
result3 = getVelocityLaplacian (authkey, dataset, time, FD4Lag4, NoTInt, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: grad2ux=%13.6e, grad2uy=%13.6e, grad2uz=%13.6e\n', p, result3(1,p), result3(2,p), result3(3,p));
end
fprintf('\nRequesting pressure at %i points...\n',npoints);
result1 = getPressure (authkey, dataset, time, Lag6, NoTInt, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: %13.6e\n', p, result1(p));
end
fprintf('\nRequesting pressure gradient at %i points...\n',npoints);
result3 = getPressureGradient (authkey, dataset, time, FD4Lag4, NoTInt, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: dpdx=%13.6e, dpdy=%13.6e, dpdz=%13.6e\n', p, result3(1,p), result3(2,p), result3(3,p));
end
fprintf('\nRequesting pressure hessian at %i points...\n',npoints);
result6 = getPressureHessian (authkey, dataset, time, FD4Lag4, NoTInt, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: d2pdxdx=%13.6e, d2pdxdy=%13.6e, d2pdxdz=%13.6e, ', p, result6(1,p), result6(2,p), result6(3,p));
fprintf(1,'d2pdydy=%13.6e, d2pdydz=%13.6e, d2pdzdz=%13.6e\n', result6(4,p), result6(5,p), result6(6,p));
end
fprintf('\nRequesting magnetic field at %i points...\n',npoints);
result3 = getMagneticField (authkey, dataset, time, Lag6, NoTInt, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: %13.6e, %13.6e, %13.6e\n', p, result3(1,p), result3(2,p), result3(3,p));
end
fprintf('\nRequesting magnetic field gradient at %i points...\n',npoints);
result9 = getMagneticFieldGradient (authkey, dataset, time, FD4Lag4, NoTInt, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: dbxdx=%13.6e, dbxdy=%13.6e, dbxdz=%13.6e, ', p, result9(1,p), result9(2,p), result9(3,p));
fprintf(1,'dbydx=%13.6e, dbydy=%13.6e, dbydz=%13.6e, ', result9(4,p), result9(5,p), result9(6,p));
fprintf(1,'dbzdx=%13.6e, dbzdy=%13.6e, dbzdz=%13.6e\n', result9(7,p), result9(8,p), result9(9,p));
end
fprintf('\nRequesting magnetic field hessian at %i points...\n',npoints);
result18 = getMagneticFieldHessian (authkey, dataset, time, FD4Lag4, NoTInt, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: d2bxdxdx=%13.6e, d2bxdxdy=%13.6e, d2bxdxdz=%13.6e, ', p, result18(1,p), result18(2,p), result18(3,p));
fprintf(1,'d2bxdydy=%13.6e, d2bxdydz=%13.6e, d2bxdzdz=%13.6e, ', result18(4,p), result18(5,p), result18(6,p));
fprintf(1,'d2bydxdx=%13.6e, d2bydxdy=%13.6e, d2bydxdz=%13.6e, ', result18(7,p), result18(8,p), result18(9,p));
fprintf(1,'d2bydydy=%13.6e, d2bydydz=%13.6e, d2bydzdz=%13.6e, ', result18(10,p), result18(11,p), result18(12,p));
fprintf(1,'d2bzdxdx=%13.6e, d2bzdxdy=%13.6e, d2bzdxdz=%13.6e, ', result18(13,p), result18(14,p), result18(15,p));
fprintf(1,'d2bzdydy=%13.6e, d2bzdydz=%13.6e, d2bzdzdz=%13.6e\n', result18(16,p), result18(17,p), result18(18,p));
end
fprintf('\nRequesting magnetic field laplacian at %i points...\n',npoints);
result3 = getMagneticFieldLaplacian (authkey, dataset, time, FD4Lag4, NoTInt, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: grad2bx=%13.6e, grad2by=%13.6e, grad2bz=%13.6e\n', p, result3(1,p), result3(2,p), result3(3,p));
end
fprintf('\nRequesting vector potential at %i points...\n',npoints);
result3 = getVectorPotential (authkey, dataset, time, Lag6, NoTInt, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: %13.6e, %13.6e, %13.6e\n', p, result3(1,p), result3(2,p), result3(3,p));
end
fprintf('\nRequesting vector potential gradient at %i points...\n',npoints);
result9 = getVectorPotentialGradient (authkey, dataset, time, FD4Lag4, NoTInt, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: daxdx=%13.6e, daxdy=%13.6e, daxdz=%13.6e, ', p, result9(1,p), result9(2,p), result9(3,p));
fprintf(1,'daydx=%13.6e, daydy=%13.6e, daydz=%13.6e, ', result9(4,p), result9(5,p), result9(6,p));
fprintf(1,'dazdx=%13.6e, dazdy=%13.6e, dazdz=%13.6e\n', result9(7,p), result9(8,p), result9(9,p));
end
fprintf('\nRequesting vector potential hessian at %i points...\n',npoints);
result18 = getVectorPotentialHessian (authkey, dataset, time, FD4Lag4, NoTInt, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: d2axdxdx=%13.6e, d2axdxdy=%13.6e, d2axdxdz=%13.6e, ', p, result18(1,p), result18(2,p), result18(3,p));
fprintf(1,'d2axdydy=%13.6e, d2axdydz=%13.6e, d2axdzdz=%13.6e, ', result18(4,p), result18(5,p), result18(6,p));
fprintf(1,'d2aydxdx=%13.6e, d2aydxdy=%13.6e, d2aydxdz=%13.6e, ', result18(7,p), result18(8,p), result18(9,p));
fprintf(1,'d2aydydy=%13.6e, d2aydydz=%13.6e, d2aydzdz=%13.6e, ', result18(10,p), result18(11,p), result18(12,p));
fprintf(1,'d2azdxdx=%13.6e, d2azdxdy=%13.6e, d2azdxdz=%13.6e, ', result18(13,p), result18(14,p), result18(15,p));
fprintf(1,'d2azdydy=%13.6e, d2azdydz=%13.6e, d2azdzdz=%13.6e\n', result18(16,p), result18(17,p), result18(18,p));
end
fprintf('\nRequesting vector potential laplacian at %i points...\n',npoints);
result3 = getVectorPotentialLaplacian (authkey, dataset, time, FD4Lag4, NoTInt, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: grad2ax=%13.6e, grad2ay=%13.6e, grad2az=%13.6e\n', p, result3(1,p), result3(2,p), result3(3,p));
end
fprintf('\nRequesting position at %i points, starting at time %f and ending at time %f...\n',npoints,startTime,endTime);
result3 = getPosition(authkey, dataset, startTime, endTime, lagDt, Lag6, 10, points);
fprintf('\nCoordinates of 10 points at startTime:\n');
for p = 1:npoints
fprintf(1,'%3i: %13.6e, %13.6e, %13.6e\n', p, points(1,p), points(2,p), points(3,p));
end
fprintf('\nCoordinates of 10 points at endTime:\n');
for p = 1:npoints
fprintf(1,'%3i: %13.6e, %13.6e, %13.6e\n', p, result3(1,p), result3(2,p), result3(3,p));
end
fprintf('\nRequesting box filter of velocity at %i points\n', npoints);
result3 = getBoxFilter(authkey, dataset, field, time, filterwidth, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: Vx=%13.6e, Vy=%13.6e, Vz=%13.6e\n', p, result3(1,p), result3(2,p), result3(3,p));
end
fprintf('\nRequesting SGS symmetric tensor at %i points\n', npoints);
result6 = getBoxFilterSGSsymtensor(authkey, dataset, field, time, filterwidth, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: xx=%13.6e, yy=%13.6e, zz=%13.6e, ', p, result6(1,p), result6(2,p), result6(3,p));
fprintf(1,'xy=%13.6e, xz=%13.6e, yz=%13.6e\n', result6(4,p), result6(5,p), result6(6,p));
end
fprintf('\nRequesting SGS for two scalar fields at %i points\n', npoints);
result1 = getBoxFilterSGSscalar(authkey, dataset, scalar_fields, time, filterwidth, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: %13.6e\n', p, result1(p));
end
fprintf('\nRequesting SGS for a vector and a scalar field at %i points\n', npoints);
result3 = getBoxFilterSGSvector(authkey, dataset, vector_scalar_fields, time, filterwidth, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: xx=%13.6e, yx=%13.6e, zx=%13.6e\n', p, result3(1,p), result3(2,p), result3(3,p));
end
fprintf('\nRequesting SGS tensor for two vector fields at %i points\n', npoints);
result9 = getBoxFilterSGStensor(authkey, dataset, vector_fields, time, filterwidth, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: xx=%13.6e, xy=%13.6e, xz=%13.6e, ', p, result9(1,p), result9(2,p), result9(3,p));
fprintf(1,'yx=%13.6e, yy=%13.6e, yz=%13.6e, ', result9(4,p), result9(5,p), result9(6,p));
fprintf(1,'zx=%13.6e, zy=%13.6e, zz=%13.6e\n', result9(7,p), result9(8,p), result9(9,p));
end
fprintf('\nRequesting box filter of velocity gradient tensor at %i points\n', npoints);
result9 = getBoxFilterGradient(authkey, dataset, field, time, filterwidth, spacing, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: duxdx=%13.6e, duxdy=%13.6e, duxdz=%13.6e, ', p, result9(1,p), result9(2,p), result9(3,p));
fprintf(1,'duydx=%13.6e, duydy=%13.6e, duydz=%13.6e, ', result9(4,p), result9(5,p), result9(6,p));
fprintf(1,'duzdx=%13.6e, duzdy=%13.6e, duzdz=%13.6e\n', result9(7,p), result9(8,p), result9(9,p));
end
fprintf('\nRequesting vorticity threshold...\n');
threshold_array = getThreshold (authkey, dataset, threshold_field, time, threshold, FD4NoInt, x_start, y_start, z_start, x_end, y_end, z_end);
for p = 1:length(threshold_array)
fprintf(1,'(%3i, %3i, %3i): %13.6e\n', threshold_array(1,p), threshold_array(2,p), threshold_array(3,p), threshold_array(4,p));
end
fprintf('\nRequesting invariant at %i points...\n',npoints);
result2 = getInvariant (authkey, dataset, time, FD4Lag4, NoTInt, npoints, points);
for p = 1:npoints
fprintf(1,'%3i: S2=%13.6e, O2=%13.6e\n', p, result2(1,p), result2(2,p));
end
% ///////////////////////////////////////////////////////////
% ////////////// GENERATE A SIMPLE CONTOUR PLOT /////////////
%////////////////////////////////////////////////////////////
% Chose a random time step
time = 0.002 * randi(1024,1);
spacing = 2.0*pi/1023;
% Set domain size and position
nx = 64;
ny = nx;
xoff = 2*pi*rand;
yoff = 2*pi*rand;
zoff = 2*pi*rand;
npoints = nx*ny;
clear points;
% Create surface
x = linspace(0, (nx-1)*spacing, nx) + xoff;
y = linspace(0, (ny-1)*spacing, ny) + yoff;
[X Y] = meshgrid(x, y);
points(1:2,:) = [X(:)'; Y(:)'];
points(3,:) = zoff;
% Get the velocity at each point
%fprintf('\nRequesting velocity at %i points...\n',npoints);
fprintf('\nRequesting velocity at (%ix%i) points for velocity contour plot...\n',nx,ny);
result3 = getVelocity(authkey, dataset, time, Lag4, NoTInt, npoints, points);
% Calculate velocity magnitude
z = sqrt(result3(1,:).^2 + result3(2,:).^2 + result3(3,:).^2);
Z = reshape(z, ny, nx);
% Plot velocity magnitude contours
contourf(X, Y, Z, 30, 'LineStyle', 'none');
set(gca, 'FontSize', 11)
title('Velocity magnitude', 'FontSize', 13, 'FontWeight', 'bold');
xlabel('x', 'FontSize', 12, 'FontWeight', 'bold');
ylabel('y', 'FontSize', 12, 'FontWeight', 'bold');
colorbar('FontSize', 12);
axis([xoff max(x) yoff max(y)]);
set(gca, 'TickDir', 'out', 'TickLength', [.02 .02],'XMinorTick', 'on', 'YMinorTick', 'on');