A multi-moment constrained finite volume model for non-hydrostatic atmospheric dynamics
Seminar Room 1, Newton Institute
Two dimensional non‐hydrostatic compressible dynamic cores for atmosphere are developed by using a new nodal type high order conservative method, so called multi‐moment constrained finite volume (MCV) method. Different from conventional finite volume method, the predicted variables (unknowns) in an MCV scheme are the values at the solution points distributed within each mesh cell. The time evolution equations to update the unknown point values are derived from a set of constraint conditions based on multi‐moment concept, where the constraint on the volume integrated average (VIA) for each mesh cell is cast into a flux form and thus guarantees rigorously the numerical conservation. Two important features makes MCV method particularly attractive as an accurate and practical numerical framework for atmospheric and oceanic modelling. 1) Using nodal values at uniformly located solution points as the predicted variables provides great convenience in de aling with complex geometry and source terms, and 2) High order schemes can be built by using constraints in terms of different moments, which makes the numerical schemes more flexible and efficient. We present in this paper the dynamic cores that use the third and the fourth order MCV schemes. We have verified the numerical outputs of both schemes by widely used standard benchmark tests and obtained competitive results. The present numerical cores provide a promising and practical framework for further development of non‐hydrostatic compressible atmospheric models.