#include #include #include #include using namespace psemek; struct water_1d_app : app::app { water_1d_app(); void update() override; void present() override; void on_resize(int width, int height) override; geom::box simulation_area; float aspect_ratio; std::size_t const N = 50; std::vector bed; std::vector height; std::vector discharge; float x(std::size_t i) const; gfx::painter painter; }; water_1d_app::water_1d_app() : app("Water 1D simulation", 4) { simulation_area[0] = {-1.f, 1.f}; simulation_area[1] = {0.f, 1.f}; bed.assign(N, 0.f); height.assign(N, 0.f); discharge.assign(N + 1, 0.f); for (std::size_t i = 0; i < N; ++i) { bed[i] += (0.5f * (N - i)) / N; bed[i] += (100.f / (N - i)) / N; // bed[i] += (0.25f * i) / N; // height[i] += (0.3f * i) / N; // height[i] = 0.3f - bed[i]; // height[i] = 0.25f; } // bed[N * 3 / 4] = 0.2f; discharge[0] = 0.04f; discharge[N] = 0.f; } void water_1d_app::update() { float const dt = 0.01f; float const dx = simulation_area[0].length() / N; float const g = 10.f; float const max_speed = 1.f; log::info() << max_speed << " " << (dx / dt); std::vector dh(N, 0.f); std::vector dq(N + 1, 0.f); for (std::size_t i = 0; i < N; ++i) { dh[i] = - (discharge[i + 1] - discharge[i]) / dx; } for (std::size_t i = 0; i < N; ++i) { height[i] += dh[i] * dt; } dh.assign(N, 0.f); for (std::size_t i = 0; i < N; ++i) { if (i != 0 && height[i] + bed[i] > bed[i - 1] && height[i - 1] + bed[i - 1] > bed[i]) dh[i] += (height[i - 1] + bed[i - 1] - height[i] - bed[i]); if (i != N - 1 && height[i] + bed[i] > bed[i + 1] && height[i + 1] + bed[i + 1] > bed[i]) dh[i] += (height[i + 1] + bed[i + 1] - height[i] - bed[i]); } for (std::size_t i = 0; i < N; ++i) { height[i] += dh[i] * 0.1f; height[i] = std::max(height[i], 0.f); } auto hu2 = [this](std::size_t i) { if (i == 0) return 0.f; if (i == N) return 0.f; if (height[i] == 0.f) return 0.f; float q = (discharge[i] + discharge[i + 1]) / 2.f; return q * q / height[i]; }; auto gh2 = [this, g](std::size_t i) { auto v = height[i] + bed[i]; return 0.5f * g * v * v; }; for (std::size_t i = 1; i < N; ++i) { dq[i] = -(hu2(i) + gh2(i) - hu2(i - 1) - gh2(i - 1)) / dx; } for (std::size_t i = 1; i < N; ++i) { discharge[i] += dq[i] * dt; // discharge[i] = (discharge[i - 1] + discharge[i + 1]) / 2.f + dq[i] * dt; // discharge[i] -= discharge[i] * dt; if (discharge[i] > 0.f) discharge[i] = std::min(discharge[i], height[i - 1] * max_speed); else discharge[i] = -std::min(-discharge[i], height[i] * max_speed); // if (height[i - 1] + bed[i - 1] < bed[i]) // discharge[i] = std::min(discharge[i], 0.f); // if (height[i] + bed[i] < bed[i - 1]) // discharge[i] = std::max(0.f, discharge[i]); } } void water_1d_app::present() { gl::ClearColor(0.8f, 0.8f, 0.8f, 0.8f); gl::Clear(gl::COLOR_BUFFER_BIT); geom::box view_area; { view_area[0] = simulation_area[0]; view_area[1] = simulation_area[1]; view_area[2] = {-1.f, 1.f}; float extra_y = view_area[1].length() * 0.1f; view_area[1].min -= extra_y; view_area[1].max += extra_y; float extra_x = view_area[1].length() * aspect_ratio - view_area[0].length(); view_area[0].min -= extra_x / 2.f; view_area[0].max += extra_x / 2.f; } geom::matrix const transform = geom::orthographic{view_area}.homogeneous_matrix(); painter.rect(simulation_area, {255, 255, 255, 255}); for (std::size_t i = 0; i < N; ++i) { painter.rect({{{x(i), x(i + 1)}, {simulation_area[1].min, simulation_area[1].min + bed[i]}}}, gfx::dark(gfx::yellow).as_color_rgba()); painter.rect({{{x(i), x(i + 1)}, {simulation_area[1].min + bed[i], simulation_area[1].min + bed[i] + height[i]}}}, gfx::blue); } for (std::size_t i = 1; i < N; ++i) { painter.line({x(i), 0.f}, {x(i), discharge[i]}, 0.005f, gfx::red); } painter.render(transform); } void water_1d_app::on_resize(int width, int height) { app::on_resize(width, height); aspect_ratio = (width * 1.f) / height; } float water_1d_app::x(std::size_t i) const { return geom::lerp(simulation_area[0], (1.f * i) / N); } int main() { return app::main(); }