Solving the 1D ‘nonlinear 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 1D ‘nonlinear advection equation’.
![\[ Q_t + \left ( \frac{Q^2}{2} \right )_x = 0 \quad \mbox{where} \quad Q=Q(x,y,t) \]](form_198_dark.png)
using a TVD Lax-Friedrichs scheme for ![$ (x,y)\in[-1,1]\times[-1,1]$](form_197_dark.png)
Definition in file HYP2DNonlinearAdvectionX.cpp.
Function Documentation
◆ main()
| int main | ( | ) |
Definition at line 76 of file HYP2DNonlinearAdvectionX.cpp.
77{
78
79 cout << "\n";
80 cout << "=== Hyperbolic: 2D nonlinear advection in x =========\n";
81 cout << "\n";
82
83 // define the domain/mesh
84 const double west = 1.0;
85 const double east = 0.0;
86 const double south = 0.0;
87 const double north = 1.0;
88 const unsigned N = 51;
91
92 Example::NlinAdv conservative_problem;
93 TwoD_TVDLF_Mesh NlinAdv_mesh( faces_x, faces_y, &conservative_problem, Example::Q_init );
94 NlinAdv_mesh.set_limiter( 0 );
95
96 double asym( 0.0 );
97 unsigned loop_counter( 0 );
98 DenseVector<double> x1( 2, 0.0 );
99 x1[ 0 ] = 0.75;
100 x1[ 1 ] = 0.5;
101 DenseVector<double> x2( 2, 0.0 );
102 x2[ 0 ] = 0.25;
103 x2[ 1 ] = 0.5;
104 do
105 {
106 NlinAdv_mesh.update( 0.49 );
107 asym = std::max( asym, std::abs( NlinAdv_mesh.get_point_values( x1 )[0] + NlinAdv_mesh.get_point_values( x2 )[0] ) );
108 ++loop_counter;
109 }
110 while ( ( NlinAdv_mesh.get_time() < 0.4 ) && ( loop_counter < 1000 ) );
111
112 // problem should be antisymmetric about x = 1/2
113 if ( ( asym > 1.e-10 ) || ( loop_counter >= 1000 ) )
114 {
115 cout << "\033[1;31;48m * FAILED \033[0m\n";
116 cout << "asymmetry = " << asym << "\n";
117 cout << "loop counter = " << loop_counter << "\n";
118 return 1;
119 }
120 else
121 {
122 cout << "\033[1;32;48m * PASSED \033[0m\n";
123 return 0;
124 }
125
126} // 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().
