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2D/CFD.h

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+#ifndef CFD_H
+#define CFD_H
+
+#include "boost/multi_array.hpp"
+
+
+#include "Class_Cell.h"
+#include "config.h"
+
+void SolutionInitializerSquareWave(boost::multi_array<Cell,2> &);
+
+void SolutionInitializerSineWave(boost::multi_array<Cell,2> &);
+
+void SolutionInitializerCircle(boost::multi_array<Cell,2> & , const int &);
+
+void GhostCellsUpdater(boost::multi_array<Cell,2> &, int &);
+
+void ReconstructVariablesFirstOrder(boost::multi_array<Cell,2> &, int &);
+
+void ReconstructVariablesBeamWarming(boost::multi_array<Cell,2> &, int &);
+
+void ReconstructVariablesLaxWendroff(boost::multi_array<Cell,2> &, int &);
+
+void ReconstructVariablesLimitedLW(boost::multi_array<Cell,2> &, int &);
+
+void ReconstructVariablesFromm(boost::multi_array<Cell,2> &, int &);
+
+void ReconstructVariablesWENO5thOrder(boost::multi_array<Cell,2> &, int &);
+
+void CalculateFlux(boost::multi_array<Cell,2> &, int &);
+
+void UpdateCellAveragesEuler(boost::multi_array<Cell,2> &, int &, double &);
+
+void UpdateCellAveragesRK2(boost::multi_array<Cell,2> &, int &, double &);
+
+void UpdateCellAveragesRK3(boost::multi_array<Cell,2> &, int &, double &);
+
+void CopyVariables(boost::multi_array<Cell,2> &);
+
+void ErrorCalculation(boost::multi_array<Cell,2> &);
+
+void UpdateCellAveragesRungeKutta2LevelSet(boost::multi_array<Cell,2> &, int &, double &);
+
+#endif

2D/Class_Cell.h

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+#ifndef CLASS_CELL_H
+#define CLASS_CELL_H
+
+#include "config.h"
+
+class Cell
+{
+public:
+    double u[NUM_RK_STEPS + 1];//talvez não dẽ
+    double uEast;
+    double uWest;
+    double uNorth;
+    double uSouth;
+    double cx;
+    double cy;
+    double dx;
+    double dy;
+    double TotalFlux;
+};
+
+#endif

2D/SolutionInitializer.h

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+#ifndef SOLUTIONINITIALIZER_H
+#define SOLUTIONINITIALIZER_H
+
+#include <cmath>
+#include "boost/multi_array.hpp"
+
+#include "config.h"
+#include "Class_Cell.h"
+
+void SolutionInitializerSquareWave(boost::multi_array<Cell,2> &cells)
+{
+    for(int i = 0; i < cells.shape()[0]; i++)
+    {
+        for(int j = 0; j < cells.shape()[1]; j++)
+        {
+            if(cells[i][j].cx > -0.25 && cells[i][j].cx < 0.25 && cells[i][j].cy > -0.25 && cells[i][j].cy < 0.25)
+            {
+                cells[i][j].u[0] = 1.0;
+            }
+            else
+            {
+                cells[i][j].u[0] = 0.0;
+            }
+        }
+    }
+}
+
+void SolutionInitializerSineWave(boost::multi_array<Cell,2> &cells)
+{
+    for(int i = 0; i < cells.shape()[0]; i++)
+    {
+        for(int j = 0; j < cells.shape()[1]; j++)
+        {
+            cells[i][j].u[0]= sin((cells[i][j].cx + cells[i][j].cy)*M_PI) / double(2);
+        }
+    }
+}
+
+#endif

2D/SolutionWriter.h

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+#ifndef SOLUTIONWRITER_H
+#define SOLUTIONWRITER_H
+
+#include<iostream>
+#include<fstream>
+#include<string>
+#include "boost/multi_array.hpp"
+
+
+#include "Class_Cell.h"
+#include "config.h"
+
+void WriteSolution(boost::multi_array<Cell,2> &cells, double &time, std::string name)
+{
+    std::ofstream out( name , std::ofstream::out);
+
+    out << "Num X cells: " << NUM_X_CELLS << std::endl;
+    out << "Num Y cells: " << NUM_Y_CELLS << std::endl;
+    out << "Num ghost cells: " << NUM_GHOST_CELLS << std::endl;
+    out << "Time: " << time << std::endl;
+
+    for(int i = 0; i < cells.shape()[0]; i++)
+    {
+        for(int j = 0; j < cells.shape()[1]; j++)
+        {
+            out << cells[i][j].cx << " " << cells[i][j].cy << " " <<cells[i][j].u[0] << std::endl;
+        }
+    }
+
+}
+
+
+#endif

2D/config.h

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+#ifndef CONFIG_H
+#define CONFIG_H
+//Macros para as constantes do problema, todas estão em unidades do sistema internacional
+
+static const unsigned int NUM_X_CELLS = 60;
+static const unsigned int NUM_Y_CELLS = 80;
+static const unsigned int NUM_GHOST_CELLS = 4;
+static const unsigned int NUM_RK_STEPS = 3;
+static const double STOPPING_TIME = 2.0;
+static const unsigned int MAX_ITERATIONS = 100000;
+static const double MAX_X_SIDE = 1.0;
+static const double MIN_X_SIDE = -1.0;
+static const double MAX_Y_SIDE = 1.0;
+static const double MIN_Y_SIDE = -1.0;
+static const double ADVECTION_VEL_X = 1.0;
+static const double ADVECTION_VEL_Y = 1.0;
+static const double COURANT_NUM = 0.5;
+#endif

2D/main.cpp

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+#include<iostream>
+#include<cstdlib>
+#include "boost/multi_array.hpp"
+
+
+using namespace std;
+using namespace boost;
+
+
+#include "Class_Cell.h"
+#include "config.h"
+
+#include "SolutionWriter.h"
+#include "CFD.h"
+
+
+int main()
+{
+    boost::multi_array<Cell,2> cells;
+    cells.resize(extents[NUM_X_CELLS + 2*NUM_GHOST_CELLS][NUM_Y_CELLS + 2*NUM_GHOST_CELLS]);//Array de objetos da classe Cell
+
+    double dx = (MAX_X_SIDE - MIN_X_SIDE) / NUM_X_CELLS;
+    double dy = (MAX_Y_SIDE - MIN_Y_SIDE) / NUM_Y_CELLS;
+    double time = 0.0;
+
+    for(int i = 0; i < cells.shape()[0]; i++)
+    {
+        for(int j = 0; j < cells.shape()[1]; j++)
+        {
+            cells[i][j].dx = dx;
+            cells[i][j].dy = dy;
+            cells[i][j].cx = MIN_X_SIDE + dx*( i + 0.5 - NUM_GHOST_CELLS );
+            cells[i][j].cy = MIN_Y_SIDE + dy*( j + 0.5 - NUM_GHOST_CELLS );
+        }
+    }
+
+    SolutionInitializerSquareWave(cells);
+
+    std::string name = "Solução no tempo " + std::to_string(time) + ".txt";
+    WriteSolution(cells,time,name);
+
+    bool LastTimeStep = false;
+
+
+    //Time step calculation
+    double dtx = (cells[0][0].dx / abs(ADVECTION_VEL_X));
+    double dty = (cells[0][0].dy / abs(ADVECTION_VEL_Y));
+    double dt = (1.0/float((1.0/float(dtx)) + (1.0/float(dty))))*COURANT_NUM;
+
+    for(int RKsteps = 0; RKsteps < NUM_RK_STEPS; RKsteps++)
+    {
+        GhostCellsUpdater(cells,RKsteps);
+        ReconstructVariablesLimitedLW(cells,RKsteps);
+        CalculateFlux(cells,RKsteps);
+        UpdateCellAveragesRK3(cells,RKsteps,dt);
+    }
+    CopyVariables(cells);
+    time += dt;
+
+    for(int timeIteration = 1; timeIteration < MAX_ITERATIONS; timeIteration++)
+    {
+        if(time + dt > STOPPING_TIME)
+        {
+            dt = STOPPING_TIME - time;
+            LastTimeStep = true;
+        }
+
+        for(int RKsteps = 0; RKsteps < NUM_RK_STEPS; RKsteps++)
+        {
+            GhostCellsUpdater(cells,RKsteps);
+            ReconstructVariablesWENO5thOrder(cells,RKsteps);
+            CalculateFlux(cells,RKsteps);
+            UpdateCellAveragesRK3(cells,RKsteps,dt);
+        }
+        CopyVariables(cells);
+        time += dt;
+
+        if(LastTimeStep){break;}
+
+        if( (timeIteration) % 25 == 0.0)
+        {
+            name = "Solução no tempo " + std::to_string(time) + ".txt";
+            WriteSolution(cells,time,name);
+        }
+
+    }
+    name = "Solução no tempo " + std::to_string(time) + ".txt";
+    WriteSolution(cells,time,name);
+    ErrorCalculation(cells);
+    return 0;
+}

2D/out/Erro.txt

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+ErrorL1 = 0.0039857
+ErrorL2 = 0.0270528
+ErrorLinf = 0.405629