Well-balanced numerical method for atmospheric flow equations with gravity

Chertock，Alina1; Kurganov，Alexander2; Wu，Tong3; Yan，Jun1

2023-02-15

10.1016/j.amc.2022.127587

APPLIED MATHEMATICS AND COMPUTATION   Impact Factor & Quartile

0096-3003

1873-5649

We are interested in simulating gravitationally stratified atmospheric flows governed by the compressible Euler equations in irregular domains. In such simulations, one of the challenges arises when the computations are conducted on a Cartesian grid. The use of regular rectangular grids that intersect with the irregular boundaries leads to the generation of arbitrarily small and highly distorted computational cells adjacent to the boundaries of the domain. The appearance of such cells may affect both the stability and efficiency of the numerical method and therefore require special attention. In order to overcome this difficulty, we introduce a structured quadrilateral mesh, which is designed for the irregular domain at hand, and solve the studied atmospheric flow equations using a second-order central-upwind scheme. In addition, the resulting numerical method is developed to provide a well-balanced discretization of the underlying system. The latter is achieved by rewriting the governing equations in terms of equilibrium variables representing perturbations of the known background equilibrium state. The proposed method is tested in a number of numerical experiments, including the buoyant bubble rising and interacting with an (zeppelin) obstacle and the Lee wave generation due to topography. The obtained numerical results demonstrate high resolution and robustness of the proposed computational approach.

Atmospheric flow equations with gravity Equilibrium variables Irregular domains Quadrilateral mesh Well-balanced central-upwind scheme

SCI

English

Corresponding

National Natural Science Foundation of China[12111530004];National Natural Science Foundation of China[12171226];National Science Foundation[DMS-1818684];National Science Foundation[DMS-2208438];

Mathematics

Mathematics, Applied

WOS:000884786500007

ELSEVIER SCIENCE INC

MATHEMATICS

2-s2.0-85140064847

Scopus

1.Department of Mathematics,North Carolina State University,Raleigh,27695,United States
2.Department of Mathematics,SUSTech International Center for Mathematics and Guangdong Provincial Key Laboratory of Computational Science and Material Design,Southern University of Science and Technology,Shenzhen,518055,China
3.Department of Mathematics,University of Texas,San Antonio,78249,United States

Chertock，Alina,Kurganov，Alexander,Wu，Tong,et al. Well-balanced numerical method for atmospheric flow equations with gravity[J]. APPLIED MATHEMATICS AND COMPUTATION,2023,439.

Chertock，Alina,Kurganov，Alexander,Wu，Tong,&Yan，Jun.(2023).Well-balanced numerical method for atmospheric flow equations with gravity.APPLIED MATHEMATICS AND COMPUTATION,439.

Chertock，Alina,et al."Well-balanced numerical method for atmospheric flow equations with gravity".APPLIED MATHEMATICS AND COMPUTATION 439(2023).