Graphs of Numerical Solutions of Benchmark problems

1. Graphs DG, Nonlinear Euler, Problems with Smooth Solutions
   Steady state solutions, flow past over a cylinder
   
2. Graphs DG, Compressible Navier Stokes
   Flow past over a cylinder
   
3. Graphs DG, Nonlinear Euler Equations Discontinuous Solutions
   Double Forward Facing Step, Double Mach Reflection
   
4. Graphs DG, Aeroacoustic Problems
   Radiation Boundary Conditions, Characteristic Boundary Conditions
   

1. Graphs DG, Nonlinear Euler, Problems with Smooth Solutions
   Steady state solutions, flow past over a cylinder
   
   Flow past over a cylinder, the Mach number computed field using P5 local polynomial space. The cylinder surface is descritized using 90 elelements.

   
   
   
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2. Graphs DG, Compressible Navier Stokes
   Flow past over a cylinder
   
   DG numerical solution of the viscous flow problem (flow past over a cylinder) using characteristic boundary conditions at the outflow boundary part of the computational domain, (toulio 2009, see mypaper 3j)

   
   
   
   
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3. Graphs DG, Nonlinear Euler Equations Discontinuous Solutions
   Double Forward Facing Step, Double Mach Reflection
   
   A new shock capturing scheme, using extrema control conditions (toulio 2009, see mypaper 8c)
   
   

   
   
   
   
   
   

   
   
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4. Graphs DG, Aeroacoustic Problems
   Radiation Boundary Conditions, Characteristic Boundary Conditions
   
   

Time harmonic source problem - Scattering by cylinder surface.
The computed pressure field using P3 local space and characteristic boundary conditions at the far field boundary part, see mypaper[3j].

Acoustic pulse scattering by a cylinder surface.
The computed pressure field using P3 local polynomial space and
characteristic boundary conditions at the boundaries, see my paper [3j].

Time harmonic source problem. Left: the pressure computed field using P3 local space using characteristic boundary conditions, Right: the variation of the L2 error measured on the boundary elements at every time step.

Propagation and reflection from a solid wall of an acoustic pulse.
The compute pressure field using radiation boundary conditions at the far field boundary parts.



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