From d25750adaeec754fbad0e79a5570ed3b5dc02513 Mon Sep 17 00:00:00 2001
From: "Claudius \"keldu\" Holeksa" <mail@keldu.de>
Date: Thu, 17 Apr 2025 18:06:54 +0200
Subject: Moved examples and added some fun rendering

---
 examples/cavity_2d.cpp | 564 +++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 564 insertions(+)
 create mode 100644 examples/cavity_2d.cpp

(limited to 'examples/cavity_2d.cpp')

diff --git a/examples/cavity_2d.cpp b/examples/cavity_2d.cpp
new file mode 100644
index 0000000..3e2e064
--- /dev/null
+++ b/examples/cavity_2d.cpp
@@ -0,0 +1,564 @@
+#include "../c++/descriptor.hpp"
+
+/**
+ */
+#include <forstio/codec/data.hpp>
+
+#include <iostream>
+#include <fstream>
+#include <cmath>
+
+namespace kel {
+namespace lbm {
+namespace sch {
+using namespace saw::schema;
+
+/**
+ * Basic distribution function
+ * Base type
+ * D
+ * Q
+ * Scalar factor
+ * D factor
+ * Q factor
+ */
+using T = Float32;
+using D2Q5 = Descriptor<2,5>;
+using D2Q9 = Descriptor<2,9>;
+
+template<typename Desc>
+using DfCell = Cell<T, Desc, 0, 0, 1>;
+
+template<typename Desc>
+using CellInfo = Cell<UInt8, D2Q9, 1, 0, 0>;
+
+/**
+ * Basic type for simulation
+ */
+template<typename Desc>
+using CellStruct = Struct<
+	Member<DfCell<Desc>, "dfs">,
+	Member<DfCell<Desc>, "dfs_old">,
+	Member<CellInfo<Desc>, "info">
+>;
+
+
+using CavityFieldD2Q9 = CellField<D2Q9, CellStruct<D2Q9>>;
+}
+
+/**
+ * Calculate the macroscopic variables rho and u in Lattice Units.
+ */
+template<typename Desc>
+void compute_rho_u (
+		saw::data<sch::DfCell<Desc>>& dfs,
+		typename saw::native_data_type<sch::T>::type& rho,
+		std::array<typename saw::native_data_type<sch::T>::type, 2>& vel
+	)
+{
+	using dfi = df_info<sch::T, Desc>;
+
+	rho = 0;
+	std::fill(vel.begin(), vel.end(), 0);
+
+	for(size_t i = 0; i < Desc::Q; ++i){
+		rho += dfs(i).get();
+		vel[0] += dfi::directions[i][0] * dfs(i).get();
+		vel[1] += dfi::directions[i][1] * dfs(i).get();
+	}
+
+	vel[0] /= rho;
+	vel[1] /= rho;
+}
+
+/**
+ * Unsure if feasible. I would have a rho normalization on the dfs and then I would use the const rho_computation
+ */
+template<typename Desc>
+void compute_const_rho_u (
+		saw::data<sch::DfCell<Desc>>& dfs,
+		const typename saw::native_data_type<sch::T>::type rho,
+		std::array<typename saw::native_data_type<sch::T>::type, 2>& vel
+	)
+{
+	using dfi = df_info<sch::T, Desc>;
+
+	saw::native_data_type<sch::T>::type real_rho = 0;
+	std::fill(vel.begin(), vel.end(), 0);
+
+	for(size_t i = 0; i < Desc::Q; ++i){
+		real_rho += dfs(i).get();
+		vel[0] += dfi::directions[i][0] * dfs(i).get();
+		vel[1] += dfi::directions[i][1] * dfs(i).get();
+	}
+	for(size_t i = 0; i < Desc::Q; ++i){
+		dfs(i).set(dfs(i).get() * (rho/real_rho));
+	}
+
+	vel[0] *= real_rho / (rho*rho);
+	vel[1] *= real_rho / (rho*rho);
+}
+
+/**
+ * Calculates the equilibrium for each direction
+ */
+template<typename Desc>
+std::array<typename saw::native_data_type<sch::T>::type,Desc::Q> equilibrium(
+	typename saw::native_data_type<sch::T>::type rho,
+	const std::array<typename saw::native_data_type<sch::T>::type, Desc::D>& vel
+){
+	using dfi = df_info<sch::T, Desc>;
+
+	typename std::array<saw::native_data_type<sch::T>::type,Desc::Q> eq;
+
+	for(std::size_t i = 0; i < eq.size(); ++i){
+		auto vel_c = (vel[0]*dfi::directions[i][0] + vel[1]*dfi::directions[i][1]);
+		auto vel_c_cs2 = vel_c * dfi::inv_cs2;
+		eq[i] = dfi::weights[i] * rho * (
+			1.0
+			+ vel_c_cs2
+			- dfi::inv_cs2 * 0.5 * ( vel[0] * vel[0] + vel[1] * vel[1] )
+			+ vel_c_cs2 * vel_c_cs2 * 0.5
+		);
+	}
+
+	return eq;
+}
+
+/**
+ * A reason for why a component based design is really good can be seen in my LR solver example
+ *
+ * Add Expression Templates and you're golden.
+ */
+template<typename Kind, typename Desc>
+class component;
+
+/*
+template<typename T, typename Encode>
+class df_cell_view;
+*/
+/**
+ * Minor helper for the AA-Pull Pattern, so I can use only one lattice
+ *
+ * Am I sure I want to use AA this way?
+ * Esoteric Twist technically reduces the needed memory access footprint
+ */
+/*
+template<typename Desc, size_t SN, size_t DN, size_t QN, typename Encode>
+class df_cell_view<sch::Cell<sch::T, Desc, SN, DN, QN>, Encode> {
+public:
+	using Schema = sch::Cell<sch::T,Desc,SN,DN,QN>;
+private:
+		std::array<std::decay_t<typename saw::native_data_type<sch::T>::type>*, QN> view_;
+public:
+		df_cell_view(const std::array<std::decay_t<typename saw::native_data_type<sch::T>::type>*, QN>& view):
+				view_{view}
+		{}
+};
+*/
+namespace cmpt {
+struct BounceBack{};
+struct MovingWall {};
+struct BGK {};
+struct ConstRhoBGK {};
+}
+
+
+/**
+ * Full-Way BounceBack. I suspect that the moving wall requires half-way bounce back.
+ */
+template<typename Desc>
+class component<cmpt::BounceBack,Desc> {
+public:
+
+	void apply(saw::data<sch::DfCell<Desc>>& dfs){
+		using dfi = df_info<sch::T,Desc>;
+
+		// Technically use .copy()
+		auto df_cpy = dfs;
+
+		for(uint64_t i = 1u; i < Desc::Q; ++i){
+			dfs({i}) = df_cpy({dfi::opposite_index.at(i)});
+		}
+	}
+};
+
+/**
+ * Full-Way moving wall Bounce back, something is not right here.
+ * Technically it should reflect properly.
+ */
+template<typename Desc>
+class component<cmpt::MovingWall, Desc> {
+public:
+	std::array<typename saw::native_data_type<sch::T>::type, Desc::D> lid_vel;
+	
+public:
+	void apply(
+		saw::data<sch::DfCell<Desc>>& dfs
+	){
+		using dfi = df_info<sch::T,Desc>;
+
+		// Technically use .copy()
+		/*
+		auto dfs_cpy = dfs;
+		
+		for(uint64_t i = 0u; i < Desc::Q; ++i){
+			dfs({dfi::opposite_index.at(i)}) = dfs_cpy({i}) - 2.0 * dfi::weights[i] * 1.0 * ( lid_vel[0] * dfi::directions[i][0] + lid_vel[1] * dfi::directions[i][1]) * dfi::inv_cs2;
+		}
+		*/
+	}
+};
+
+template<typename Desc>
+class component<cmpt::BGK, Desc> {
+public:
+	typename saw::native_data_type<sch::T>::type relaxation_;
+public:
+	void apply(saw::data<sch::DfCell<Desc>>& dfs){
+		typename saw::native_data_type<sch::T>::type rho;
+		std::array<typename saw::native_data_type<sch::T>::type, Desc::D> vel;
+		compute_rho_u<Desc>(dfs,rho,vel);
+		auto eq = equilibrium<Desc>(rho,vel);
+		
+		for(uint64_t i = 0u; i < Desc::Q; ++i){
+			dfs({i}).set(dfs({i}).get() + (1.0 / relaxation_) * (eq[i] - dfs({i}).get()));
+		}
+	}
+};
+
+template<typename Desc>
+class component<cmpt::ConstRhoBGK, Desc> {
+public:
+	typename saw::native_data_type<sch::T>::type relaxation_;
+	typename saw::native_data_type<sch::T>::type rho_;
+public:
+	void apply(saw::data<sch::DfCell<Desc>>& dfs){
+		std::array<typename saw::native_data_type<sch::T>::type, Desc::D> vel;
+		compute_const_rho_u<Desc>(dfs,rho_,vel);
+		auto eq = equilibrium<Desc>(rho_,vel);
+		
+		for(uint64_t i = 0u; i < Desc::Q; ++i){
+			dfs({i}).set(dfs({i}).get() + (1.0 / relaxation_) * (eq[i] - dfs({i}).get()));
+		}
+	}
+};
+}
+}
+
+constexpr size_t dim_size = 2;
+constexpr size_t dim_x = 128;
+constexpr size_t dim_y = 128;
+
+
+template<typename Func>
+void apply_for_cells(Func&& func, saw::data<kel::lbm::sch::CavityFieldD2Q9>& dat){
+	for(std::size_t i = 0; i < dat.meta().at({1u}).get(); ++i){
+		for(std::size_t j = 0; j < dat.meta().at({0u}).get(); ++j){
+			saw::data<saw::schema::UInt64> di{i};
+			saw::data<saw::schema::UInt64> dj{j};
+			auto& cell_v = dat({{dj,di}});
+			func(cell_v, j, i);
+		}
+	}
+}
+
+void set_geometry(saw::data<kel::lbm::sch::CavityFieldD2Q9>& latt){
+	using namespace kel::lbm;
+	apply_for_cells([](auto& cell, std::size_t i, std::size_t j){
+		uint8_t val = 0;
+		if(j == 1){
+			val = 2u;
+		}
+		if(i == 1 || (i+2) == dim_x || (j+2) == dim_y){
+			val = 3u;
+		}
+		if(i > 1 && (i+2) < dim_x && j > 1 && (j+2) < dim_y){
+			val = 1u;
+		}
+		if(i == 0 || j == 0 || (i+1) == dim_x || (j+1) == dim_y){
+			val = 0u;
+		}
+		cell.template get<"info">()(0u).set(val);
+	}, latt);
+}
+
+void set_initial_conditions(saw::data<kel::lbm::sch::CavityFieldD2Q9>& latt){
+	using namespace kel::lbm;
+	
+	typename saw::native_data_type<sch::T>::type rho = 1.0;
+	{
+		std::array<typename saw::native_data_type<sch::T>::type, sch::D2Q9::D> vel = {0.0, 0.0};
+		auto eq = equilibrium<sch::D2Q9>(rho, vel);
+
+		apply_for_cells([&eq](auto& cell, std::size_t i, std::size_t j){
+			(void) i;
+			(void) j;
+			auto& dfs = cell.template get<"dfs">();
+			auto& dfs_old = cell.template get<"dfs_old">();
+			auto info = cell.template get<"info">()(0u).get();
+			for(uint64_t k = 0; k < sch::D2Q9::Q; ++k){
+				dfs(k).set(eq[k]);
+				dfs_old(k).set(eq[k]);
+			}
+		}, latt);
+	}
+	
+	{
+		std::array<typename saw::native_data_type<sch::T>::type, sch::D2Q9::D> vel = {0.1, 0.0};
+		auto eq = equilibrium<sch::D2Q9>(rho, vel);
+
+		apply_for_cells([&eq](auto& cell, std::size_t i, std::size_t j){
+			(void) i;
+			(void) j;
+			auto& dfs = cell.template get<"dfs">();
+			auto& dfs_old = cell.template get<"dfs_old">();
+			auto info = cell.template get<"info">()(0u).get();
+			if(info == 2u){
+				for(uint64_t k = 0; k < sch::D2Q9::Q; ++k){
+					dfs(k).set(eq[k]);
+					dfs_old(k).set(eq[k]);
+				}
+			}
+		}, latt);
+	}
+}
+
+void lbm_step(
+	saw::data<kel::lbm::sch::CavityFieldD2Q9>& latt,
+	bool even_step
+){
+	using namespace kel::lbm;
+  using dfi = df_info<sch::T,sch::D2Q9>;
+
+	component<cmpt::BGK,sch::D2Q9> coll;
+	coll.relaxation_ = 0.5384;
+	component<cmpt::ConstRhoBGK,sch::D2Q9> rho_coll;
+	rho_coll.relaxation_ = 0.5384;
+	rho_coll.rho_ = 1.0;
+
+	component<cmpt::BounceBack,sch::D2Q9> bb;
+	component<cmpt::MovingWall,sch::D2Q9> bb_lid;
+	bb_lid.lid_vel = {0.1,0.0};
+
+	// Collide
+	apply_for_cells([&](auto& cell, std::size_t i, std::size_t j){
+		auto& df = even_step ? cell.template get<"dfs_old">() : cell.template get<"dfs">();
+		auto& info = cell.template get<"info">();
+
+		auto info_val = info({0u}).get();
+		switch(info_val){
+		case 1u:
+			coll.apply(df);
+			break;
+		case 2u:
+			// bb.apply(df);
+			bb_lid.apply(df);
+			break;
+		case 3u:
+			bb.apply(df);
+			break;
+		}
+	}, latt);
+
+	// Stream
+	for(uint64_t i = 1; (i+1) < latt.template get_dim_size<0>().get(); ++i){
+		for(uint64_t j = 1; (j+1) < latt.template get_dim_size<1>().get(); ++j){
+			auto& cell = latt({{i,j}});
+			auto& df_new = even_step ? cell.template get<"dfs">() : cell.template get<"dfs_old">();
+			auto& info_new = cell.template get<"info">();
+
+			if(info_new({0u}).get() > 0u && info_new({0u}).get() != 2u){
+				for(uint64_t k = 0u; k < sch::D2Q9::Q; ++k){
+					auto dir = dfi::directions[dfi::opposite_index[k]];
+					auto& cell_dir_old = latt({{i+dir[0],j+dir[1]}});
+					
+					auto& df_old = even_step ? cell_dir_old.template get<"dfs_old">() : cell_dir_old.template get<"dfs">();
+					auto& info_old = cell_dir_old.template get<"info">();
+
+					if( info_old({0}).get() == 2u ){
+						auto& df_old_loc = even_step ? latt({{i,j}}).template get<"dfs_old">() : latt({{i,j}}).template get<"dfs">();
+						df_new({k}) = df_old_loc({dfi::opposite_index.at(k)}) - 2.0 * dfi::inv_cs2 * dfi::weights.at(k) * 1.0 * ( bb_lid.lid_vel[0] * dir[0] + bb_lid.lid_vel[1] * dir[1]);
+						// dfs({dfi::opposite_index.at(i)}) = dfs_cpy({i}) - 2.0 * dfi::weights[i] * 1.0 * ( lid_vel[0] * dfi::directions[i][0] + lid_vel[1] * dfi::directions[i][1]) * dfi::inv_cs2;
+					} else {
+						df_new({k}) = df_old({k});
+					}
+				}
+			}
+		}
+	}
+}
+
+int main(){
+	using namespace kel::lbm;
+
+	saw::data<sch::FixedArray<sch::UInt64,sch::D2Q9::D>> dim{{dim_x, dim_y}};
+
+	saw::data<sch::CavityFieldD2Q9, saw::encode::Native> lattice{dim};
+
+	// auto& df_field = lattices.at(0).template get<"dfs">();
+	//for(uint64_t i = 0; i < df_field.get_dim_size<0u>(); ++i){
+	//	lattices.at(i) = {dim_x, dim_y};
+	//}
+
+	/**
+	 * Set meta information describing what this cell is
+	 */
+	set_geometry(lattice);
+	/**
+	 * 
+	 */
+	set_initial_conditions(lattice);
+
+	/**
+	 * Timeloop
+	 */
+
+	/**
+	 * Print basic setup info
+	 */
+	apply_for_cells([](auto& cell, std::size_t i, std::size_t j){
+			// Not needed
+			(void) j;
+			std::cout<<(static_cast<uint32_t>(cell.template get<"info">()({0}).get()));
+			if( (i+1) < dim_x){
+				std::cout<<" ";
+			}else{
+				std::cout<<"\n";
+			}
+	}, lattice);
+	
+	uint64_t lattice_steps = 512000u;
+	bool even_step = true;
+
+	uint64_t print_every = 256u;
+	uint64_t file_no = 0u;
+
+	for(uint64_t step = 0; step < lattice_steps; ++step){
+
+		if(step % print_every == 0u){
+			std::cout<<"\n";
+			typename saw::native_data_type<sch::T>::type sum = 0.0;
+
+
+			apply_for_cells([&](auto& cell, std::size_t i, std::size_t j){
+				auto& dfs = cell.template get<"dfs">();
+				typename saw::native_data_type<sch::T>::type rho;
+				std::array<typename saw::native_data_type<sch::T>::type, sch::D2Q9::D> vel;
+				compute_rho_u<sch::D2Q9>(dfs,rho,vel);
+
+				if(i > 1 && (i+2) < dim_x && j > 1 && (j+2) < dim_y){
+					sum += rho;
+				}
+				auto angle = std::atan2(vel[1],vel[0]);
+				double vel_mag = vel[1] * vel[1] + vel[0] * vel[0];
+			
+				auto dir_char = [&]() -> std::string_view {
+					/**
+					 * Flipped y due to print order
+					 */
+					constexpr auto pi = M_PI;
+					return "■";
+					if(vel_mag < 1e-4){
+						return "•";
+					}
+					if(angle > 7.0 / 8.0 * pi){
+						return "←";
+					}
+					if(angle > 5.0 / 8.0 * pi){
+						return "↙";
+					}
+					if(angle > 3.0 / 8.0 * pi){
+						return "↓";
+					}
+					if(angle > 1.0 / 8.0 * pi){
+						return "↘";
+					}
+					if(angle > -1.0 / 8.0 * pi){
+						return "→";
+					}
+					if(angle > -3.0 / 8.0 * pi){
+						return "↗";
+					}
+					if(angle > -5.0 / 8.0 * pi){
+						return "↑";
+					}
+					if(angle > -7.0 / 8.0 * pi){
+						return "↖";
+					}
+					return "←";
+				}();
+
+				std::array<uint32_t,3u> rgb_start{64,64,255};
+				std::array<uint32_t,3u> rgb_stop{255,64,64};
+				std::array<uint32_t,3u> rgb_middle{255,255,255};
+
+
+				auto col_interpol = [&](){
+					std::array<uint32_t, 3u> rgb_interpol = rgb_start;
+					double vel_mag_cut = std::min(1.0,std::max(vel_mag/(0.07*0.07),0.0));
+
+					if(vel_mag_cut < 0.5){
+						uint32_t vel_mag_i = static_cast<uint32_t>(2.0 * vel_mag_cut * 256);
+						for(uint8_t i = 0u; i < 3u; ++i){
+							rgb_interpol[i] = (rgb_middle[i] * vel_mag_i + (256-vel_mag_i) * rgb_start[i]) / 256;
+						}
+					}else{
+						uint32_t vel_mag_i = static_cast<uint32_t>((2.0*(vel_mag_cut-0.5)) * 256);
+						for(uint8_t i = 0u; i < 3u; ++i){
+							rgb_interpol[i] = (rgb_stop[i] * vel_mag_i + (256-vel_mag_i) * rgb_middle[i]) / 256;
+						}
+					}
+					return rgb_interpol;
+				};
+				auto rgb_interpol = col_interpol();
+
+				std::cout<<"\x1b[38;2;"<<rgb_interpol[0]<<";"<<rgb_interpol[1]<<";"<<rgb_interpol[2]<<"m"<<dir_char;
+				if( (i+1) < dim_x){
+					std::cout<<" ";
+				}else{
+					std::cout<<"\n";
+				}
+			}, lattice);
+			std::cout<<"\x1b[38;2;255;255;255m";
+
+			/// std::cout<<"Average rho: "<<(sum / ((dim_x-4)*(dim_y-4)))<<std::endl;
+			std::cout.flush();
+
+			std::ofstream vtk_file{"tmp/cavity_2d_"+std::to_string(file_no)+".vtk"};
+
+			vtk_file <<"# vtk DataFile Version 3.0\n";
+			vtk_file <<"Velocity Cavity2D example\n";
+			vtk_file <<"ASCII\n";
+			vtk_file <<"DATASET STRUCTURED_POINTS\n";
+			vtk_file <<"DIMENSIONS "<< dim_x <<" "<<dim_y<<" 1\n";
+			vtk_file <<"SPACING 1.0 1.0 1.0\n";
+			vtk_file <<"ORIGIN 0.0 0.0 0.0\n";
+			vtk_file <<"POINT_DATA "<<(dim_x*dim_y)<<"\n";
+			vtk_file <<"VECTORS Velocity float\n";
+			
+			apply_for_cells([&](auto& cell, std::size_t i, std::size_t j){
+				auto dfs = even_step ? cell.template get<"dfs_old">() : cell.template get<"dfs">();
+
+				typename saw::native_data_type<sch::T>::type rho;
+				std::array<typename saw::native_data_type<sch::T>::type, sch::D2Q9::D> vel;
+				compute_rho_u<sch::D2Q9>(dfs,rho,vel);
+
+				vtk_file << static_cast<float>(vel[0u]) << " " << static_cast<float>(vel[1u])<<" 0.0\n";
+			}, lattice);
+			
+
+			++file_no;
+		}
+		
+		lbm_step(lattice, even_step);
+
+		even_step = !even_step;
+	}
+
+	/**
+	 * Flush cout
+	 */
+	std::cout<<"\n\n";
+	std::cout.flush();
+	return 0;
+}
-- 
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