void step()
{
phi.initGhostCells( );
{
#pragma omp parallel for firstprivate( ghostfield)
for( unsigned i=0; i<2; i++)
{
swap_fields( field[i], ghostfield);// now field is void
ghostfield.initGhostCells( );
arakawa( phi, ghostfield, nonlinear[i]);
swap_fields( field[i], ghostfield);// now ghostfield is void
}
karniadakis.step_i<S>( field, nonlinear);
#pragma omp parallel for
for( unsigned i=0; i<2; i++)
dft_drt.r2c( field[i], cfield[i]);
karniadakis.step_ii( cfield);
swap_fields( cphi, phi); //now phi is void
multiply_coefficients();
#pragma omp parallel for
for( unsigned i=0; i<2; i++)
dft_drt.c2r( cfield[i], field[i]);
}
dft_drt.c2r( cphi, phi); //field in phi again
}
int main()
{
//Construct coefficients and init karniadakis with correct normalisation
const Complex kxmin { 0, 2.*M_PI/lx}, kzmin{ 0, M_PI/lz};
for( unsigned i=0; i<nz; i++)
for( unsigned j=0; j<nx/2+1; j++)
rayleigh_equations( coefficients(i,j), (double)j*kxmin, (double)(i+1)*kzmin);
karniadakis.init_coeff( coefficients, (double)(2*nx*(nz))); //swaps in coefficients
//Initialize the complex fields ////////////////////////
cfield[0].zero();
cfield[1].zero();
Complex ctheta_0 = { 0, -0.5*theta_0};
Complex comega_0 = {0.5*omega_0, 0};
cfield[0](iz, ix) = ctheta_0;
cfield[1](iz, ix) = comega_0;
//Transform and backtransform will multiply input
dft_drt.c2r( cfield[0], field[0]), dft_drt.c2r( cfield[1], field[1]);
dft_drt.r2c( field[0], cfield[0]), dft_drt.r2c( field[1], cfield[1]);
//Hopefully the step_ii function will correctly normalize
karniadakis.invert_coeff<TL_EULER>();
karniadakis.step_ii( cfield);
if( abs( cfield[0](iz,ix) - ctheta_0) > 1e-14 ||
abs( cfield[1](iz,ix) - comega_0) > 1e-14 )
{
cout << "TEST FAILED: \n";
cout << setprecision(6) << fixed;
cout << "Rayleigh = "<< R <<endl;
cout << "-0.5 theta_0 = " <<ctheta_0<< endl
<< " 0.5 omega_0 = "<< comega_0<<endl;
cout << cfield[0](iz,ix) << endl<< cfield[1](iz,ix)<<endl;
cout <<scientific<< "Difference: " <<abs( cfield[0](iz,ix) - ctheta_0 )<<endl;
cout <<scientific<< "Difference: " <<abs( cfield[1](iz,ix) - comega_0 )<<endl;
}
else
cout << "TEST PASSED!\n";
return 0;
}
int main()
{
////////////////////////////////glfw//////////////////////////////
GLFWwindow* w = draw::glfwInitAndCreateWindow( 800, 200, "Behold the convection!");
draw::RenderHostData render(1,1);
draw::ColorMapRedBlueExt colors( R);
std::vector<double> visual;
//////////////////////////////////////////////////////////////////
const Complex kxmin { 0, 2.*M_PI/lx}, kzmin{ 0, M_PI/lz};
TurbulentBath bath(R);
for( unsigned i=0; i<nz; i++)
for( unsigned j=0; j<nx/2+1; j++)
{
rayleigh_equations( coefficients(i,j), (double)j*kxmin, (double)(i+1)*kzmin);
laplace_inverse( cphi_coefficients(i,j), (double)j*kxmin, (double)(i+1)*kzmin);
cfield[0](i,j) ={ bath( coefficients(i,j)(0,0).real()), bath( coefficients(i,j)(0,0).real())};
}
//init solvers
karniadakis.init_coeff( coefficients, prefactor); //swaps in coefficients
//init fields
cfield[1].zero();
cphi.zero();
multiply_coefficients();
dft_drt.c2r( cfield[0], field[0]);
dft_drt.c2r( cfield[1], field[1]);
dft_drt.c2r( cphi, phi);
//first steps
karniadakis.invert_coeff<TL_EULER>();
step<TL_EULER>();
karniadakis.invert_coeff<TL_ORDER2>();
step<TL_ORDER2>();
karniadakis.invert_coeff<TL_ORDER3>();
step<TL_ORDER3>();
//////////////////////////////////////////////////////////////////
double timer[10];
Timer t;
static int i=0;
cout << "PRESS ESC OR CLOSE WINDOW TO TERMINATE PROGRAM!\n";
while( !glfwWindowShouldClose( w))
{
visual = field[0].copy();
render.renderQuad( visual, nx, nz, colors);
glfwPollEvents();
glfwSwapBuffers( w );
//////////////call stepper///////////////////////////////////
t.tic();
for( unsigned j=0; j<N; j++)
step<TL_ORDER3>();
t.toc();
timer[i++%10] = t.diff();
//////////////////////////////////////////////////////////////
}
double avg = 0;
for( int i=0; i<10; i++)
avg+=timer[i]/10./(double)N;
cout << "Average time for one step: " << avg << "s\n";
cout << "Total number of steps: " << i*N << "\n";
glfwTerminate();
//////////////////////////////////////////////////////////////////
fftw_cleanup();
return 0;
}
