An asymptotic preserving scheme for the two-dimensional shallow water equations with Coriolis forces

Liu, Xin1; Chertock, Alina2; Kurganov, Alexander1,3

2019-08-15

10.1016/j.jcp.2019.04.035

JOURNAL OF COMPUTATIONAL PHYSICS   Impact Factor & Quartile

0021-9991

1090-2716

We consider the two-dimensional Saint-Venant system of shallow water equations with Coriolis forces. We focus on the case of a low Froude number, in which the system is stiff and conventional explicit numerical methods are extremely inefficient and often impractical. Our goal is to design an asymptotic preserving (AP) scheme, which is uniformly asymptotically consistent and stable for a broad range of (low) Froude numbers. The goal is achieved using the flux splitting proposed in [Haack et al., Commun. Comput. Phys., 12 (2012), pp. 955-980] in the context of isentropic Euler and Navier-Stokes equations. We split the flux into the stiff and nonstiff parts and then use an implicit-explicit approach: apply an explicit hyperbolic solver (we use the second-order central-upwind scheme) to the nonstiff part of the system while treating the stiff part of it implicitly. Moreover, the stiff part of the flux is linear and therefore we reduce the implicit stage of the proposed method to solving a Poisson-type elliptic equation, which is discretized using a standard second-order central difference scheme.

Saint-Venant system of shallow water equations Coriolis forces Asymptotic preserving scheme Central-upwind scheme Flux splitting Implicit-explicit approach

SCI ; EI

English

First

NSFC[11771201]

Computer Science ; Physics

Computer Science, Interdisciplinary Applications ; Physics, Mathematical

WOS:000469209800013

ACADEMIC PRESS INC ELSEVIER SCIENCE

20201708548592

Coriolis force ; Numerical methods ; Froude number ; Poisson equation

Fluid Flow, General:631.1 ; Calculus:921.2 ; Numerical Methods:921.6 ; Mechanics:931.1

PHYSICS

Web of Science

1.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China
2.North Carolina State Univ, Dept Math, Raleigh, NC 27695 USA
3.Tulane Univ, Math Dept, New Orleans, LA 70118 USA

Liu, Xin,Chertock, Alina,Kurganov, Alexander. An asymptotic preserving scheme for the two-dimensional shallow water equations with Coriolis forces[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2019,391:259-279.

Liu, Xin,Chertock, Alina,&Kurganov, Alexander.(2019).An asymptotic preserving scheme for the two-dimensional shallow water equations with Coriolis forces.JOURNAL OF COMPUTATIONAL PHYSICS,391,259-279.

Liu, Xin,et al."An asymptotic preserving scheme for the two-dimensional shallow water equations with Coriolis forces".JOURNAL OF COMPUTATIONAL PHYSICS 391(2019):259-279.