HyPar
1.0
FiniteDifference HyperbolicParabolic PDE Solver on Cartesian Grids

The following are some examples that use the reducedorder modeling capabilities implemented in the libROM library (https://www.librom.net/). To run them, HyPar needs to be compiled with libROM. Familiarity with using libROM and the mathematical concepts implemented in it is assumed.
Note:
These examples may come with a Python script to plot the solutions from the binary solution file. This script will need the environment variable HYPAR_DIR (/path/to/hypar) to be defined, so make sure this variable exists.
The following examples demonstrate training a DMDROMObject using the solutions from a PDE simulation. The same procedure (i.e. providing the libROM input file librom.inp with the appropriate inputs) can be used with any other simulation.
1D Linear Advection  Sine Wave
1D Linear Advection  Discontinuous Waves (Time Windowed DMD)
1D Euler Equations  Sod Shock Tube (Time Windowed DMD)
1D Euler Equations  ShuOsher Problem (Time Windowed DMD)
2D Euler Equations  Isentropic Vortex Convection
2D Euler Equations  Riemann Problem Case 4 (Time Windowed DMD)
2D Euler Equations (with gravitational force)  Rising Thermal Bubble (TimeWindowed DMD)
2D Euler Equations (with gravitational force)  InertiaGravity Waves (TimeWindowed DMD) with PETSc IMEX time integration (Requires PETSc)
2D NavierStokes Equations  LidDriven Square Cavity (TimeWindowed DMD)
2D (1D1V) Vlasov Equation  TwoStream Instability (TimeWindowed DMD)
3D NavierStokes  Steady, incompressible, viscous flow around a cylinder (TimeWindowed DMD)
3D NavierStokes  Unsteady, incompressible, viscous flow around a cylinder with vortex shedding (TimeWindowed DMD)
3D NavierStokes  Inviscid ShockCylinder Interaction (TimeWindowed DMD)
3D NavierStokes Equations (with gravitational force)  Rising Thermal Bubble (TimeWindowed DMD) with PETSc IMEX time integration (Requires PETSc)
The following examples demonstrate using a trained DMDROMObject to compute the solution instead of the discretizing the PDE in space and time. The same steps (i.e. providing the libROM input file librom.inp and trained DMD objects consistent with the computational domain) can be used for any other simulation.
1D Linear Advection  Sine Wave
1D Linear Advection  Discontinuous Waves (Time Windowed DMD)
1D Euler Equations  Sod Shock Tube (Time Windowed DMD)
2D Euler Equations  Isentropic Vortex Convection
2D NavierStokes Equations  LidDriven Square Cavity (TimeWindowed DMD)
2D (1D1V) Vlasov Equation  TwoStream Instability (TimeWindowed DMD)
3D NavierStokes  Steady, incompressible, viscous flow around a cylinder (TimeWindowed DMD)
3D NavierStokes  Inviscid ShockCylinder Interaction (TimeWindowed DMD)