A hybrid pseudo-incompressible–hydrostatic model

The pseudo-incompressible approximation, which assumes small pressure perturbations from a one-dimensional reference state, has long been used to model large-scale dynamics in stellar and planetary atmospheres. However, existing implementations do not conserve energy when the state is time-dependent. We use variational formulation derive an energy-conserving evolves while remaining hydrostatic. present algorithm for solving these equations case of closed boundaries, velocity constraint degenerate. implement within low-Mach-number code MAESTROeX, validate it against fully compressible several test cases, finding that our hybrid pseudo-incompressible–hydrostatic generally shows better agreement with results than MAESTROeX implementation.