The following are some examples are simulated using the sparse grids method. Familiarity with the sparse grids approach (specifically the combination technique approach) is assumed.

2D Linear Advection - Sine Wave
2D Linear Advection - Sine Wave with Spatially-Varying Advection Speed

2D Euler Equations - Density Sine Wave
2D Euler Equations - Isentropic Vortex Convection
2D Euler Equations (with gravitational force) - Rising Thermal Bubble

Any other simulation can also be run with the sparse grids method (as long as the number of spatial dimensions is greater than 1); only the following is needed:

Input file sparse_grids.inp that specifies parameters related to the sparse grids method.

As for the output, instead of op*.*, the full grid solution will be written to op_fg*.*, and it will be in the same format/structure as the op*.* files. If specified in the inputs, the sparse grid solution files will also be written to op_sg_<n>*.*.

Note: Sparse grids work well with smooth, linear simulations. Adapting them for hyperbolic simulations with shocks and discontinuities is an area of active research.