Alfven test case using the same parameters as Fluxo

Author: ranocha

examples/ideal_MHD_alfven_fluxo.m

@@ -0,0 +1,87 @@
+%clc
+clear
+close all
+
+addpath('../matlab')
+
+BalanceLaws.prepare_vars();
+global I_Mesh I_TI I_BalanceLaws I_Tech I_RunOps I_Results
+
+% Alfven wave testcase used in [Fluxo](https://github.com/project-fluxo/fluxo), domain [-1,1]^3.
+N = uint32(40);
+I_Mesh('NODES_X') = N; I_Mesh('NODES_Y') = N; I_Mesh('NODES_Z') = uint32(5);
+I_Mesh('XMIN') = -1.0; I_Mesh('XMAX') = 1.0;
+I_Mesh('YMIN') = -1.0; I_Mesh('YMAX') = 1.0;
+I_Mesh('ZMIN') = -1.0; I_Mesh('ZMAX') = 1.0;
+
+I_TI('final_time') = 125;
+I_TI('cfl') = 0.4;
+
+dt = I_TI('cfl') * 2.0 / double(I_Mesh('NODES_Y'));
+num_steps = ceil(I_TI('final_time')/dt);
+dt = I_TI('final_time') / num_steps;
+
+%Time integrator: SSPRK33 SSPRK104 CalvoFrancoRandez2R64
+%KennedyCarpenterLewis2R54C CarpenterKennedy2N54 ToulorgeDesmet2N84F
+I_TI('time_integrator') = 'CarpenterKennedy2N54';
+
+I_TI('DT') = dt;
+I_TI('num_steps') = num_steps;
+
+I_Tech('device') = 1;
+I_Tech('REAL') = 'double'; % float, double
+I_Tech('REAL4') = sprintf('%s4',I_Tech('REAL')); %Vector datatype
+I_Tech('memory_layout') = 'USE_STRUCTURE_OF_ARRAYS'; % USE_ARRAY_OF_STRUCTURES, USE_STRUCTURE_OF_ARRAYS
+
+% Use as kernel defines to keep consistency with header files?
+I_BalanceLaws('NUM_CONSERVED_VARS') = 8;
+I_BalanceLaws('NUM_AUXILIARY_VARS') = 4;
+I_BalanceLaws('NUM_TOTAL_VARS') = I_BalanceLaws('NUM_CONSERVED_VARS') + I_BalanceLaws('NUM_AUXILIARY_VARS');
+
+%Compiler based optimizations
+if strcmp(I_Tech('REAL'),'float')
+    I_Tech('optimizations') = ' -cl-mad-enable -cl-no-signed-zeros -cl-finite-math-only -cl-single-precision-constant';
+else
+    I_Tech('optimizations') = ' -cl-mad-enable -cl-no-signed-zeros -cl-finite-math-only';
+end
+
+I_RunOps('periodic') = 'USE_PERIODIC'; % 'NONE', 'USE_PERIODIC'; must be set to 'USE_PERIODIC'
+                                       % if periodic boundary conditions should be used
+
+I_RunOps('order') = 6; I_RunOps('operator_form') = 'classical'; % order: 2, 4, 6; operator_form: classical, extended
+I_RunOps('conservation_laws') = 'ideal_MHD';
+I_RunOps('testcase') = 'alfven_fluxo';
+I_RunOps('plot_numerical_solution') = 'z';
+I_RunOps('save_integrals_over_time') = false;
+% Choose between L2 and LInfinity norm for error calculation
+I_RunOps('norm') = 'LInf'; % L2, LInf
+%% Initialize variables
+[field_u1, field_u2] = BalanceLaws.initialize();
+
+fprintf('Testcase: %s \nOrder: %d \nTime integrator: %s\nDT: %.16e   N_STEPS: %5d   FINAL_TIME: %.16e\nDX: %.16e   NODES_X: %5d\nDY: %.16e   NODES_Y: %5d\nDZ: %.16e   NODES_Z: %5d \nREAL: %s\n\n',...
+        I_RunOps('testcase'), I_RunOps('order'), I_TI('time_integrator'), I_TI('DT'), I_TI('num_steps'), I_TI('final_time'), I_Mesh('DX'), I_Mesh('NODES_X'), I_Mesh('DY'), I_Mesh('NODES_Y'), I_Mesh('DZ'), I_Mesh('NODES_Z'), I_Tech('REAL'));
+%% Compute numerical solution
+BalanceLaws.compute_numerical_solution(field_u1, field_u2);
+fprintf('Total runtime: %.3f seconds   Kernel runtime: %d\n',  I_Results('runtime'), I_Results('kernel_runtime'));
+
+rel_err = I_Results('rel_err');
+for comp=0:I_BalanceLaws('NUM_CONSERVED_VARS') - 1
+    fprintf('Relative Error of Field Component %d: %.15f %%\n', comp, 100*rel_err(comp + 1))
+end
+
+%% Plot numerical solution
+num_nodes = I_Mesh('NODES_X')*I_Mesh('NODES_Y')*I_Mesh('NODES_Z');
+if strcmp(I_Tech('memory_layout'), 'USE_ARRAY_OF_STRUCTURES')
+    field_u1_plot = reshape(field_u1(1:num_nodes*I_BalanceLaws('NUM_TOTAL_VARS')), [I_BalanceLaws('NUM_TOTAL_VARS'), num_nodes]);
+elseif strcmp(I_Tech('memory_layout'), 'USE_STRUCTURE_OF_ARRAYS')
+    field_u1_tmp = reshape(field_u1, I_Tech('NUM_NODES_PAD'), I_BalanceLaws('NUM_TOTAL_VARS'));
+    field_u1_plot = field_u1_tmp(1:num_nodes, :)';
+else
+    error('You must USE_ARRAY_OF_STRUCTURES or USE_STRUCTURE_OF_ARRAYS.')
+end
+
+%Optional plots
+if ismember(lower(char(I_RunOps('plot_numerical_solution'))),{'x','y','z','xy', 'xz', 'yz', 'xyz'})
+    plot_2D(field_u1_plot, I_RunOps('plot_numerical_solution'),...
+        I_Mesh('NODES_X'), I_Mesh('NODES_Y'), I_Mesh('NODES_Z'), 'Numerical Solution', 6, 8);
+end

include_testcases/ideal_MHD_alfven_fluxo.h

@@ -0,0 +1,110 @@
+// This project is licensed under the terms of the Creative Commons CC BY-NC-ND 4.0 license.
+
+//--------------------------------------------------------------------------------------------------
+// Functions for field initialisation
+//--------------------------------------------------------------------------------------------------
+
+/*
+Alfven wave testcase used in [Fluxo](https://github.com/project-fluxo/fluxo), domain [-1,1]^3.
+*/
+
+// paramters of the Alfven wave test case
+#define CONST_FREQUENCY 1
+REAL constant CONST_omega = 6.283185307179586 * CONST_FREQUENCY;
+REAL constant CONST_r = 2; // lenght-variable = lenght of computational domain
+REAL constant CONST_e = 0.2; // epsilon = 0.2
+
+/*
+Analytical solution of the velocity field.
+*/
+inline REAL4 u_analytical(uint ix, uint iy, uint iz, REAL time) {
+
+  REAL x = (REAL)XMIN + ix*(REAL)DX;
+  REAL y = (REAL)YMIN + iy*(REAL)DY;
+  REAL z = (REAL)ZMIN + iz*(REAL)DZ;
+
+  REAL nx = rsqrt(CONST_r*CONST_r + 1);
+  REAL ny = CONST_r * rsqrt(CONST_r*CONST_r + 1);
+  REAL sqr = 1;
+  REAL Va = CONST_omega / (ny * sqr);
+  REAL phi_alv = CONST_omega / ny * (nx * (x - 0.5*CONST_r) + ny * (y - 0.5*CONST_r)) - Va * time;
+
+  REAL u1 = - CONST_e * ny * cos(phi_alv);
+  REAL u2 =   CONST_e * nx * cos(phi_alv);
+  REAL u3 =   CONST_e * sin(phi_alv);
+
+  return (REAL4) {u1, u2, u3, (REAL)(0)};
+}
+
+/*
+Analytical solution of the magnetic field.
+*/
+inline REAL4 b_analytical(uint ix, uint iy, uint iz, REAL time) {
+
+  REAL x = (REAL)XMIN + ix*(REAL)DX;
+  REAL y = (REAL)YMIN + iy*(REAL)DY;
+  REAL z = (REAL)ZMIN + iz*(REAL)DZ;
+
+  REAL nx = rsqrt(CONST_r*CONST_r + 1);
+  REAL ny = CONST_r * rsqrt(CONST_r*CONST_r + 1);
+  REAL sqr = 1;
+  REAL Va = CONST_omega / (ny * sqr);
+  REAL phi_alv = CONST_omega / ny * (nx * (x - 0.5*CONST_r) + ny * (y - 0.5*CONST_r)) - Va * time;
+
+  REAL B1 = nx + CONST_e * ny * cos(phi_alv) * sqr;
+  REAL B2 = ny - CONST_e * nx * cos(phi_alv) * sqr;
+  REAL B3 =    - CONST_e * sin(phi_alv) * sqr;
+
+  return (REAL4) {B1, B2, B3, (REAL)(0)};
+}
+
+/*
+Boundary condition of the magnetic field.
+*/
+inline REAL4 b_boundary(uint ix, uint iy, uint iz, REAL time) {
+
+  return b_analytical(ix, iy, iz, time);
+}
+
+/*
+Boundary condition of the velocity field.
+*/
+inline REAL4 u_boundary(uint ix, uint iy, uint iz, REAL time) {
+
+  return u_analytical(ix, iy, iz, time);
+}
+
+
+/* Boundary condition of the pressure and density */
+
+inline REAL p_boundary(uint ix, uint iy, uint iz, REAL time) {
+
+  return (REAL)(1);
+}
+
+inline REAL rho_boundary(uint ix, uint iy, uint iz, REAL time) {
+
+  return (REAL)(1);
+}
+
+
+/* initial conditions for the simulation */
+
+inline REAL4 b_initial(uint ix, uint iy, uint iz, REAL time){
+
+  return b_analytical(ix, iy, iz, time);
+}
+
+inline REAL4 u_initial(uint ix, uint iy, uint iz, REAL time){
+
+  return u_analytical(ix, iy, iz, time);
+}
+
+inline REAL p_initial(uint idx, uint iy, uint iz, REAL time){
+  return (REAL)(1);
+}
+
+inline REAL rho_initial(uint idx, uint iy, uint iz, REAL time){
+
+  return (REAL)(1);
+}