Function update

examples/pde/boltzmann_cfd.cpp:370–405

* @brief Updates the velocity field, density and strain at each point in the * grid * */

 *
 */
void update(Simulation& sim) {
    auto& ux    = sim.ux;
    auto& uy    = sim.uy;
    auto& rho   = sim.rho;
    auto& sigma = sim.sigma;
    auto& f     = sim.f;
    auto& feq   = sim.feq;
    auto& ex    = sim.ex;
    auto& ey    = sim.ey;

    auto e_tile = af::join(3, af::constant(1, 1, 1, 9), ex, ey);
    auto result = af::sum(f * e_tile, 2);

    rho = result(af::span, af::span, af::span, 0);
    result /= rho;
    ux = result(af::span, af::span, af::span, 1);
    uy = result(af::span, af::span, af::span, 2);

    // Above code equivalent to
    // rho = af::sum(f, 2);
    // ux = af::sum(f * ex, 2) / rho;
    // uy = af::sum(f * ey, 2) / rho;

    auto product   = f - feq;
    auto e_product = af::join(3, ex * ex, ex * ey * std::sqrt(2), ey * ey);

    sigma = af::sqrt(af::sum(af::pow(af::sum(product * e_product, 2), 2), 3));

    // Above code equivalent to

    // auto xx = af::sum(product * ex * ex, 2);
    // auto xy = af::sum(product * ex * ey, 2);
    // auto yy = af::sum(product * ey * ey, 2);

    // sigma = af::sqrt(xx * xx + xy * xy * 2 + yy * yy);
}

af::array generate_image(size_t width, size_t height, const Simulation& sim) {
    const auto& ux         = sim.ux;