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#include <iostream>
#include <numeric>
#include <iostream>
#include <fstream>
#include <memory>
#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 }
};
}
}
constexpr std::size_t dimX = 256;
constexpr std::size_t dimY = dimX;
constexpr double uLid = 0.1;
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
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