The following are some basic examples that are simulated using HyPar. They all use explicit time integration, and do not require HyPar to be compiled with any external libraries.

1D Linear Advection - Sine Wave
1D Linear Advection - Sine Wave with Spatially-Varying Advection Speed
1D Linear Advection - Discontinuous Waves
1D Linear Diffusion - Sine Wave

1D Inviscid Burgers Equation - Sine Wave

1D Euler Equations - Sod Shock Tube
1D Euler Equations - Lax Shock Tube
1D Euler Equations - Shu-Osher Problem
1D Euler Equations - Sod Shock Tube with Gravitational Force

1D Shallow Water Equations - Dam Breaking over Rectangular Bump

2D Linear Advection - Gaussian Pulse
2D Linear Advection - Sine Wave with Spatially-Varying Advection Speed
2D Linear Diffusion - Sine Wave

2D Inviscid Burgers Equation - Sine Wave

2D (1D-1V) Vlasov Equation - Prescribed E-Field
2D (1D-1V) Vlasov Equation - Two-Stream Instability
2D (1D-1V) Vlasov Equation - Landau Damping

2D Euler Equations - Riemann Problem Case 4
2D Euler Equations - Riemann Problem Case 6
2D Euler Equations - Radial Expansion Wave
2D Euler Equations - Isentropic Vortex Convection

2D Euler Equations (with gravitational force) - Inertia-Gravity Waves
2D Euler Equations (with gravitational force) - Rising Thermal Bubble

2D Navier-Stokes Equations - Lid-Driven Square Cavity
2D Navier-Stokes Equations - Laminar Flow over Flat Plate

2D Shallow Water Equations - Circular Dam Break
2D Shallow Water Equations - Latitude Belt Flow

3D Linear Advection - Gaussian Pulse

3D Navier-Stokes Equations - Isotropic Turbulence Decay
3D Navier-Stokes Equations - Rising Thermal Bubble

3D NUMA (Nonhydrostatic Unified Model of the Atmosphere) Equations - Rising Thermal Bubble