High order discretely well-balanced methods for arbitrary hydrostatic atmospheres. (arXiv:2005.01811v4 [math.NA] UPDATED)
<a href="http://arxiv.org/find/math/1/au:+Berberich_J/0/1/0/all/0/1">Jonas P. Berberich</a>, <a href="http://arxiv.org/find/math/1/au:+Kappeli_R/0/1/0/all/0/1">Roger Käppeli</a>, <a href="http://arxiv.org/find/math/1/au:+Chandrashekar_P/0/1/0/all/0/1">Praveen Chandrashekar</a>, <a href="http://arxiv.org/find/math/1/au:+Klingenberg_C/0/1/0/all/0/1">Christian Klingenberg</a>
We introduce novel high order well-balanced finite volume methods for the
full compressible Euler system with gravity source term. They require no a
priori knowledge of the hydrostatic solution which is to be well-balanced and
are not restricted to certain classes of hydrostatic solutions. In one spatial
dimension we construct a method that exactly balances a high order
discretization of any hydrostatic state. The method is extended to two spatial
dimensions using a local high order approximation of a hydrostatic state in
each cell. The proposed simple, flexible, and robust methods are not restricted
to a specific equation of state. Numerical tests verify that the proposed
method improves the capability to accurately resolve small perturbations on
hydrostatic states.
We introduce novel high order well-balanced finite volume methods for the
full compressible Euler system with gravity source term. They require no a
priori knowledge of the hydrostatic solution which is to be well-balanced and
are not restricted to certain classes of hydrostatic solutions. In one spatial
dimension we construct a method that exactly balances a high order
discretization of any hydrostatic state. The method is extended to two spatial
dimensions using a local high order approximation of a hydrostatic state in
each cell. The proposed simple, flexible, and robust methods are not restricted
to a specific equation of state. Numerical tests verify that the proposed
method improves the capability to accurately resolve small perturbations on
hydrostatic states.
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