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-rw-r--r--boltz.cc322
-rw-r--r--src/boundary_conditions.h48
-rw-r--r--src/box_obstacle.h36
-rw-r--r--src/data_cell.h23
-rw-r--r--src/data_cell_buffer.h50
-rw-r--r--src/fluid_buffer.h91
-rw-r--r--src/lbm.h81
-rw-r--r--src/vector.h2
8 files changed, 368 insertions, 285 deletions
diff --git a/boltz.cc b/boltz.cc
index e36e337..6f8788e 100644
--- a/boltz.cc
+++ b/boltz.cc
@@ -1,117 +1,10 @@
#include <iostream>
-#include <numeric>
-#include <iostream>
-#include <fstream>
-#include <memory>
#include <vector>
#include <algorithm>
-#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]);
- }
-};
-
-using Velocity = Vector<double>;
-using Density = double;
-
-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)
- };
- }
-};
-
-class CellBuffer {
- private:
- const std::size_t dim_x_;
- const std::size_t dim_y_;
-
- std::unique_ptr<Cell[]> curr_;
- std::unique_ptr<Cell[]> prev_;
-
- public:
- CellBuffer(std::size_t dimX, std::size_t dimY):
- dim_x_(dimX),
- dim_y_(dimY),
- curr_(new Cell[dimX*dimY]),
- prev_(new Cell[dimX*dimY]) { }
-
- void swap() {
- curr_.swap(prev_);
- }
-
- inline Cell& curr(std::size_t x, std::size_t y) {
- return curr_[y*dim_x_ + x];
- }
-
- inline Cell& curr(Vector<std::size_t> pos) {
- return curr(pos[0], pos[1]);
- }
-
- inline Cell& prev(std::size_t x, std::size_t y) {
- return prev_[y*dim_x_ + x];
- }
-
- inline Cell& prev(Vector<std::size_t> pos) {
- return prev(pos[0], pos[1]);
- }
-};
-
-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 }
- };
- }
-}
+#include "lbm.h"
+#include "boundary_conditions.h"
+#include "box_obstacle.h"
constexpr std::size_t dimX = 120;
constexpr std::size_t dimY = dimX;
@@ -122,110 +15,8 @@ constexpr double reynolds = 1000;
constexpr double tau = 3 * uLid * (dimX-1) / reynolds + 0.5;
constexpr double omega = 1. / tau;
-CellBuffer pop(dimX, dimY);
-
-Density density [dimX][dimY];
-Velocity velocity[dimX][dimY];
-
-void streamFluidCell(std::size_t x, std::size_t y) {
- if ( x != 0 && x != dimX - 1 && y != 0 && y != 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+i >= 0 && x+i <= dimX - 1 && y+j >= 0 && y+j <= dimY - 1 ) {
- pop.curr(x+i,y+j).get(i,j) = pop.prev(x,y).get(i,j);
- }
- }
- }
- }
-}
-
-void collideFluidCell(std::size_t x, std::size_t y) {
- // compute equilibrium
- Cell eq;
- eq.equilibrize(density[x][y], velocity[x][y]);
-
- // collide (BGK, relax towards equilibrium)
- if ( x != 0 && x != dimX - 1 && y != 0 && y != 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+i >= 0 && x+i <= dimX - 1 && y+j >= 0 && y+j <= 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));
- }
- }
- }
- }
-}
-
-void computeWallCell(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(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);
-}
-
-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() const {
- for ( std::size_t x = lower_x_+1; x < upper_x_; ++x ) {
- computeWallCell({x, lower_y_}, { 0,-1});
- computeWallCell({x, upper_y_}, { 0, 1});
- }
- for ( std::size_t y = lower_y_+1; y < upper_y_; ++y ) {
- computeWallCell({lower_x_, y}, {-1, 0});
- computeWallCell({upper_x_, y}, { 1, 0});
- }
- computeWallCell({lower_x_, lower_y_}, {-1,-1});
- computeWallCell({upper_x_, lower_y_}, { 1,-1});
- computeWallCell({upper_x_, upper_y_}, { 1, 1});
- computeWallCell({lower_x_, upper_y_}, {-1, 1});
- }
-};
+DataCellBuffer pop(dimX, dimY);
+FluidBuffer fluid(dimX, dimY);
std::vector<BoxObstacle> obstacles{
{20, 20, 40, 40},
@@ -239,108 +30,69 @@ std::vector<BoxObstacle> obstacles{
{80, 80, 100, 100},
};
-void computeLbmStep(std::size_t t) {
+void init() {
+ for ( std::size_t x = 0; x < dimX; ++x ) {
+ for ( std::size_t y = 0; y < dimY; ++y ) {
+ fluid.density(x,y) = 1.0;
+ fluid.velocity(x,y) = { 0.0, 0.0 };
+
+ static_cast<Cell&>(pop.curr(x,y)).equilibrize(
+ fluid.density(x,y), fluid.velocity(x,y));
+ static_cast<Cell&>(pop.prev(x,y)).equilibrize(
+ fluid.density(x,y), fluid.velocity(x,y));
+ }
+ }
+}
+
+void computeLbmStep() {
pop.swap();
for ( std::size_t x = 0; x < dimX; ++x ) {
for ( std::size_t y = 0; y < dimY; ++y ) {
- if ( std::all_of(obstacles.cbegin(), obstacles.cend(), [x, y](const auto& o) -> bool {
+ if ( std::all_of(obstacles.cbegin(), obstacles.cend(), [x, y](const auto& o) {
return !o.isInside(x, y);
}) ) {
- streamFluidCell(x, y);
+ streamFluidCell(pop, x, y);
}
}
}
// straight wall cell bounce back
for ( std::size_t x = 0; x < dimX; ++x ) {
- computeZouHeVelocityWallCell({x, dimY-1}, { 0,-1}, uLid);
+ computeZouHeVelocityWallCell(pop, {x, dimY-1}, { 0,-1}, uLid);
}
for ( std::size_t x = 1; x < dimX-1; ++x ) {
- computeWallCell({x, 0}, { 0, 1});
+ computeWallCell(pop, {x, 0}, { 0, 1});
}
for ( std::size_t y = 1; y < dimY-1; ++y ) {
- computeWallCell({0, y}, { 1, 0});
- computeWallCell({dimX-1, y}, {-1, 0});
+ computeWallCell(pop, {0, y}, { 1, 0});
+ computeWallCell(pop, {dimX-1, y}, {-1, 0});
}
// edge wall cell bounce back
- computeWallCell({0, 0 }, { 1, 1});
- computeWallCell({dimX-1, 0 }, {-1, 1});
+ computeWallCell(pop, {0, 0 }, { 1, 1});
+ computeWallCell(pop, {dimX-1, 0 }, {-1, 1});
// obstacles
- for ( auto& o : obstacles ) {
- o.applyBoundary();
+ for ( const auto& box : obstacles ) {
+ box.applyBoundary(pop);
}
for ( std::size_t x = 0; x < dimX; ++x ) {
for ( std::size_t y = 0; y < dimY; ++y ) {
- density[x][y] = pop.curr(x,y).sum();
- velocity[x][y] = pop.curr(x,y).velocity(density[x][y]);
+ Cell& cell = static_cast<Cell&>(pop.curr(x,y));
+ fluid.density(x,y) = cell.sum();
+ fluid.velocity(x,y) = cell.velocity(fluid.density(x,y));
- if ( std::all_of(obstacles.cbegin(), obstacles.cend(), [x, y](const auto& o) -> bool {
+ if ( std::all_of(obstacles.cbegin(), obstacles.cend(), [x, y](const auto& o) {
return !o.isInside(x, y);
}) ) {
- collideFluidCell(x, y);
+ collideFluidCell(omega, pop, fluid, x, y);
}
}
}
}
-void init() {
- for ( std::size_t x = 0; x < dimX; ++x ) {
- for ( std::size_t y = 0; y < dimY; ++y ) {
- velocity[x][y] = { 0.0, 0.0 };
- density[x][y] = 1.0;
-
- pop.curr(x,y).equilibrize(density[x][y], velocity[x][y]);
- pop.prev(x,y).equilibrize(density[x][y], velocity[x][y]);
- }
- }
-}
-
-void writeCurrentStateAsVTK(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();
-}
-
int main() {
init();
@@ -349,12 +101,12 @@ int main() {
std::cout << "tau: " << tau << std::endl;
for ( std::size_t t = 0; t <= 6000; ++t ) {
- computeLbmStep(t);
+ computeLbmStep();
if ( t % 100 == 0 ) {
std::cout << ".";
std::cout.flush();
- writeCurrentStateAsVTK(t);
+ fluid.writeAsVTK(t);
}
}
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 {