Young Researchers Workshop: Current trends in kinetic theory

High-order well-balanced FVM for Euler equations with gravity

Luc Grosheintz-Laval



Hydrostatic equilibrium is a stationary, non-constant solution of the Euler equations. In this equilibrium the pressure gradient is balanced by gravity. This force balance determines, to first order, the structure of earth's atmosphere, stellar atmospheres and the ocean. Effects such as weather can be understood as a (small) perturbation from hydrostatic equilibrium. Since this equilibrium is non-constant in space, classical FVM methods will not preserve this equilibrium exactly. I'll present a high-order FVM which balances hydrostatic equilibria to machine precision. This is joint work with Roger Kaeppeli, Siddhartha Mishra.