Bring in some more structure

7 files changed, 331 insertions, 0 deletions

diff --git a/src/boundary_conditions.h b/src/boundary_conditions.h
new file mode 100644
index 0000000..c825c32
--- /dev/null
+++ b/src/boundary_conditions.h
@@ -0,0 +1,48 @@
+#pragma once
+
+#include "vector.h"
+#include "data_cell_buffer.h"
+
+std::pair<Vector<int>, Vector<int>> neighbors(Vector<int> v) {
+	if ( v[0] == 0 ) {
+		return {
+			{ -1, v[1] },
+			{  1, v[1] }
+		};
+	} else if ( v[1] == 0 ) {
+		return {
+			{ v[0], -1 },
+			{ v[0],  1 }
+		};
+	} else {
+		return {
+			{    0, v[1] },
+			{ v[0], 0    }
+		};
+	}
+}
+
+void computeWallCell(DataCellBuffer& pop, Vector<std::size_t> cell, Vector<int> normal) {
+	const auto [neighborA, neighborB] = neighbors(normal);
+
+	pop.curr(cell).get(neighborA) = pop.curr(cell).get(-neighborA);
+	pop.curr(cell).get(normal   ) = pop.curr(cell).get(-normal   );
+	pop.curr(cell).get(neighborB) = pop.curr(cell).get(-neighborB);
+}
+
+void computeZouHeVelocityWallCell(DataCellBuffer& pop, Vector<std::size_t> cell, Vector<int> normal, double vX) {
+	const auto [neighborA, neighborB] = neighbors(normal);
+
+	const double rho = pop.curr(cell).get(-1,0) + pop.curr(cell).get(0,0) + pop.curr(cell).get(1,0)
+		+ 2.*(
+			pop.curr(cell).get(-neighborA) +
+			pop.curr(cell).get(-normal   ) +
+			pop.curr(cell).get(-neighborB)
+		);
+
+	pop.curr(cell).get(neighborA) = pop.curr(cell).get(-neighborA)
+	                              + 0.5*( pop.curr(cell).get( 1,0) - pop.curr(cell).get(-1,0) - vX*rho );
+	pop.curr(cell).get(normal   ) = pop.curr(cell).get(-normal   );
+	pop.curr(cell).get(neighborB) = pop.curr(cell).get(-neighborB)
+	                              + 0.5*( pop.curr(cell).get(-1,0) - pop.curr(cell).get( 1,0) + vX*rho );
+}
diff --git a/src/box_obstacle.h b/src/box_obstacle.h
new file mode 100644
index 0000000..46660a7
--- /dev/null
+++ b/src/box_obstacle.h
@@ -0,0 +1,36 @@
+#pragma once
+
+#include "data_cell_buffer.h"
+#include "boundary_conditions.h"
+
+struct BoxObstacle {
+	const std::size_t lower_x_;
+	const std::size_t lower_y_;
+	const std::size_t upper_x_;
+	const std::size_t upper_y_;
+
+	BoxObstacle(std::size_t lX, std::size_t lY, std::size_t uX, std::size_t uY):
+		lower_x_(lX), lower_y_(lY), upper_x_(uX), upper_y_(uY) { }
+
+	bool isInside(std::size_t x, std::size_t y) const {
+		return x > lower_x_
+		    && x < upper_x_
+		    && y > lower_y_
+		    && y < upper_y_;
+	}
+
+	void applyBoundary(DataCellBuffer& pop) const {
+		for ( std::size_t x = lower_x_+1; x < upper_x_; ++x ) {
+			computeWallCell(pop, {x, lower_y_}, { 0,-1});
+			computeWallCell(pop, {x, upper_y_}, { 0, 1});
+		}
+		for ( std::size_t y = lower_y_+1; y < upper_y_; ++y ) {
+			computeWallCell(pop, {lower_x_, y}, {-1, 0});
+			computeWallCell(pop, {upper_x_, y}, { 1, 0});
+		}
+		computeWallCell(pop, {lower_x_, lower_y_}, {-1,-1});
+		computeWallCell(pop, {upper_x_, lower_y_}, { 1,-1});
+		computeWallCell(pop, {upper_x_, upper_y_}, { 1, 1});
+		computeWallCell(pop, {lower_x_, upper_y_}, {-1, 1});
+	}
+};
diff --git a/src/data_cell.h b/src/data_cell.h
new file mode 100644
index 0000000..fbb5dfb
--- /dev/null
+++ b/src/data_cell.h
@@ -0,0 +1,23 @@
+#pragma once
+
+#include "vector.h"
+
+struct DataCell {
+	double data[3][3];
+
+	inline double& get(int x, int y) {
+		return data[1+x][1-y];
+	}
+
+	inline double& get(Vector<int> v) {
+		return get(v[0], v[1]);
+	}
+
+	inline double get(int x, int y) const {
+		return data[1+x][1-y];
+	}
+
+	inline double get(Vector<int> v) const {
+		return get(v[0], v[1]);
+	}
+};
diff --git a/src/data_cell_buffer.h b/src/data_cell_buffer.h
new file mode 100644
index 0000000..06c2644
--- /dev/null
+++ b/src/data_cell_buffer.h
@@ -0,0 +1,50 @@
+#pragma once
+
+#include <memory>
+
+#include "data_cell.h"
+
+class DataCellBuffer {
+	private:
+		const std::size_t dim_x_;
+		const std::size_t dim_y_;
+
+		std::unique_ptr<DataCell[]> curr_;
+		std::unique_ptr<DataCell[]> prev_;
+
+	public:
+		DataCellBuffer(std::size_t dimX, std::size_t dimY):
+			dim_x_(dimX),
+			dim_y_(dimY),
+			curr_(new DataCell[dimX*dimY]),
+			prev_(new DataCell[dimX*dimY]) { }
+
+		std::size_t dimX() const {
+			return dim_x_;
+		}
+
+		std::size_t dimY() const {
+			return dim_y_;
+		}
+
+		void swap() {
+			curr_.swap(prev_);
+		}
+
+		inline DataCell& curr(std::size_t x, std::size_t y) {
+			return curr_[y*dim_x_ + x];
+		}
+
+		inline DataCell& curr(Vector<std::size_t> pos) {
+			return curr(pos[0], pos[1]);
+		}
+
+		inline DataCell& prev(std::size_t x, std::size_t y) {
+			return prev_[y*dim_x_ + x];
+		}
+
+		inline DataCell& prev(Vector<std::size_t> pos) {
+			return prev(pos[0], pos[1]);
+		}
+};
+
diff --git a/src/fluid_buffer.h b/src/fluid_buffer.h
new file mode 100644
index 0000000..a6c41ba
--- /dev/null
+++ b/src/fluid_buffer.h
@@ -0,0 +1,91 @@
+#pragma once
+
+#include <fstream>
+#include <memory>
+
+#include "vector.h"
+
+using Velocity = Vector<double>;
+using Density  = double;
+
+class FluidBuffer {
+	private:
+		const std::size_t dim_x_;
+		const std::size_t dim_y_;
+
+		std::unique_ptr<Density[]> density_;
+		std::unique_ptr<Velocity[]> velocity_;
+
+	public:
+		FluidBuffer(std::size_t dimX, std::size_t dimY):
+			dim_x_(dimX),
+			dim_y_(dimY),
+			density_(new Density[dimX*dimY]),
+			velocity_(new Velocity[dimX*dimY]) { }
+
+		std::size_t dimX() const {
+			return dim_x_;
+		}
+
+		std::size_t dimY() const {
+			return dim_y_;
+		}
+
+		Density& density(std::size_t x, std::size_t y) {
+			return density_[y*dim_x_ + x];
+		}
+
+		Density& curr(Vector<std::size_t> pos) {
+			return density(pos[0], pos[1]);
+		}
+
+		Velocity& velocity(std::size_t x, std::size_t y) {
+			return velocity_[y*dim_x_ + x];
+		}
+
+		Velocity& velocity(Vector<std::size_t> pos) {
+			return velocity(pos[0], pos[1]);
+		}
+
+		void writeAsVTK(int time) {
+			std::ofstream fout;
+			fout.open(("result/data_t" + std::to_string(time) + ".vtk").c_str());
+
+			fout << "# vtk DataFile Version 3.0\n";
+			fout << "lbm_output\n";
+			fout << "ASCII\n";
+			fout << "DATASET RECTILINEAR_GRID\n";
+			fout << "DIMENSIONS " << dimX() << " " << dimY() << " 1" << "\n";
+
+			fout << "X_COORDINATES " << dimX() << " float\n";
+			for( std::size_t x = 0; x < dimX(); ++x ) {
+				fout << x << " ";
+			}
+
+			fout << "\nY_COORDINATES " << dimY() << " float\n";
+			for( std::size_t y = 0; y < dimY(); ++y ) {
+				fout << y << " ";
+			}
+
+			fout << "\nZ_COORDINATES " << 1 << " float\n";
+			fout << 0 << "\n";
+			fout << "POINT_DATA " << dimX() * dimY() << "\n";
+
+			fout << "VECTORS velocity float\n";
+			for ( std::size_t y = 0; y < dimY(); ++y ) {
+				for ( std::size_t x = 0; x < dimX(); ++x ) {
+					fout << velocity(x,y)[0] << " " << velocity(x,y)[1] << " 0\n";
+				}
+			}
+
+			fout << "SCALARS density float 1\n";
+			fout << "LOOKUP_TABLE default\n";
+			for ( std::size_t y = 0; y < dimY(); ++y ) {
+				for ( std::size_t x = 0; x < dimX(); ++x ) {
+					fout << density(x,y) << "\n";
+				}
+			}
+
+			fout.close();
+		}
+};
diff --git a/src/lbm.h b/src/lbm.h
new file mode 100644
index 0000000..685fa08
--- /dev/null
+++ b/src/lbm.h
@@ -0,0 +1,81 @@
+#pragma once
+
+#include "data_cell.h"
+#include "data_cell_buffer.h"
+#include "fluid_buffer.h"
+
+constexpr DataCell weight{
+	1./36., 1./9., 1./36.,
+	1./9.,  4./9., 1./9.,
+	1./36., 1./9., 1./36
+};
+
+struct Cell : DataCell {
+	void equilibrize(Density d, Velocity v) {
+		for ( int i = -1; i <= 1; ++i ) {
+			for ( int j = -1; j <= 1; ++j ) {
+				get(i,j) = weight.get(i,j) * d * (1 + 3*v.comp(i,j) + 4.5*sq(v.comp(i,j)) - 1.5*sq(v.norm()));
+			}
+		}
+	}
+
+	double sum() const {
+		return get(-1, 1) + get( 0, 1) + get( 1, 1) + get(-1, 0) + get( 0, 0) + get( 1, 0) + get(-1,-1) + get( 0,-1) + get( 1,-1);
+	}
+
+	Velocity velocity(Density d) const {
+		return 1./d * Velocity{
+			get( 1, 0) - get(-1, 0) + get( 1, 1) - get(-1,-1) + get( 1,-1) - get(-1,1),
+			get( 0, 1) - get( 0,-1) + get( 1, 1) - get(-1,-1) - get( 1,-1) + get(-1,1)
+		};
+	}
+};
+
+void streamFluidCell(DataCellBuffer& pop, std::size_t x, std::size_t y) {
+	if ( x != 0 && x != pop.dimX()-1 && y != 0 && y != pop.dimY()-1 ) {
+		// stream internal cells
+		for ( int i = -1; i <= 1; ++i ) {
+			for ( int j = -1; j <= 1; ++j ) {
+				pop.curr(x+i,y+j).get(i,j) = pop.prev(x,y).get(i,j);
+			}
+		}
+	} else {
+		// stream boundary cells,
+		// missing populations to be determined by boundary conditions
+		for ( int i = -1; i <= 1; ++i ) {
+			for ( int j = -1; j <= 1; ++j ) {
+				if ( (x > 0 || i >= 0) && x+i <= pop.dimX()-1 && (y > 0 || j >= 0) && y+j <= pop.dimY()-1 ) {
+					pop.curr(x+i,y+j).get(i,j) = pop.prev(x,y).get(i,j);
+				}
+			}
+		}
+	}
+}
+
+void collideFluidCell(
+	double omega,
+	DataCellBuffer& pop, FluidBuffer& fluid,
+	std::size_t x, std::size_t y) {
+	// compute equilibrium
+	Cell eq;
+	eq.equilibrize(fluid.density(x,y), fluid.velocity(x,y));
+
+	// collide (BGK, relax towards equilibrium)
+	if ( x != 0 && x != pop.dimX()-1 && y != 0 && y != pop.dimY()-1 ) {
+		for ( int i = -1; i <= 1; ++i ) {
+			for ( int j = -1; j <= 1; ++j ) {
+				pop.curr(x,y).get(i,j) = pop.curr(x,y).get(i,j) + omega * (eq.get(i,j) - pop.curr(x,y).get(i,j));
+			}
+		}
+	} else {
+		// partial collide for boundary cells
+		for ( int i = -1; i <= 1; ++i ) {
+			for ( int j = -1; j <= 1; ++j ) {
+				if ( (x > 0 || i >= 0) && x+i <= pop.dimX()-1 && (y > 0 || j >= 0) && y+j <= pop.dimY()-1 ) {
+					pop.curr(x,y).get(i,j) = pop.curr(x,y).get(i,j) + omega * (eq.get(i,j) - pop.curr(x,y).get(i,j));
+				}
+			}
+		}
+	}
+}
+
diff --git a/src/vector.h b/src/vector.h
index 3a3ed5c..5e105c4 100644
--- a/src/vector.h
+++ b/src/vector.h
@@ -1,3 +1,5 @@
+#pragma once
+
 #include <cmath>
 
 inline double sq(double x) noexcept {