Solving the 2D advection equation. More...
#include <TwoD_HYP_bundle.h>Go to the source code of this file.
Classes | |
| class | CppNoddy::Example::NlinAdv |
| Define the system. More... | |
Namespaces | |
| namespace | CppNoddy |
| A collection of OO numerical routines aimed at simple (typical) applied problems in continuum mechanics. | |
| namespace | CppNoddy::Example |
Functions | |
| void | CppNoddy::Example::Q_init (const double &x, const double &y, DenseVector< double > &q) |
| Set the initial state of the system. More... | |
| int | main () |
Detailed Description
Solving the 2D advection equation.
![\[ Q_t + \left ( \frac{Q}{\sqrt{2}} \right )_x + \left ( \frac{Q}{\sqrt{2}} \right )_y= 0 \quad \mbox{where} \quad Q=Q(x,y,t) \]](form_196_dark.png)
using a TVD Lax-Friedrichs scheme for ![$ (x,y)\in[-1,1]\times[-1,1]$](form_197_dark.png)
Definition in file HYP2DLinearAdvectionXY.cpp.
Function Documentation
◆ main()
| int main | ( | ) |
Definition at line 65 of file HYP2DLinearAdvectionXY.cpp.
66{
67
68 cout << "\n";
69 cout << "=== Hyperbolic: 2D linear advection at an angle =====\n";
70 cout << "\n";
71
72 // define the domain/mesh
73 const double west = 1.0;
74 const double east = -1.0;
75 const double south = -1.0;
76 const double north = 1.0;
77 const unsigned N = 51;
80
81 Example::NlinAdv conservative_problem;
82 TwoD_TVDLF_Mesh NlinAdv_mesh( faces_x, faces_y, &conservative_problem, Example::Q_init );
83 NlinAdv_mesh.set_limiter( 1 );
84
85 double asym( 0.0 );
86 unsigned loop_counter( 0 );
87 DenseVector<double> x1( 2, 0.0 );
88 x1[ 0 ] = 0.2;
89 x1[ 1 ] = 0.4;
90 DenseVector<double> x2( 2, 0.0 );
91 x2[ 0 ] = 0.4;
92 x2[ 1 ] = 0.2;
93 do
94 {
95 NlinAdv_mesh.update( 0.49 );
96 asym = std::max( asym, std::abs( NlinAdv_mesh.get_point_values( x1 )[0] - NlinAdv_mesh.get_point_values( x2 )[0] ) );
97 ++loop_counter;
98 }
99 while ( ( NlinAdv_mesh.get_time() < 1.0 ) && ( loop_counter < 20 ) );
100
101 // problem should be antisymmetric about y = x
102 if ( ( asym > 5.e-10 ) || ( loop_counter >= 1000 ) )
103 {
104 cout << "\033[1;31;48m * FAILED \033[0m\n";
105 cout << "asymmetry = " << asym << "\n";
106 cout << "loop counter = " << loop_counter << "\n";
107 return 1;
108 }
109 else
110 {
111 cout << "\033[1;32;48m * PASSED \033[0m\n";
112 return 0;
113 }
114
115} // end of main()
Definition: TwoD_TVDLF_Mesh.h:19
DenseVector< double > uniform_node_vector(const double &lower, const double &upper, const std::size_t &N)
Return a DENSE vector with the nodal points of a uniform mesh distributed between the upper/lower bou...
Definition: Utility.cpp:113
References CppNoddy::TwoD_TVDLF_Mesh::get_point_values(), CppNoddy::TwoD_TVDLF_Mesh::get_time(), CppNoddy::TwoD_TVDLF_Mesh::set_limiter(), CppNoddy::Utility::uniform_node_vector(), and CppNoddy::TwoD_TVDLF_Mesh::update().
