Discontinuous Galerkin method for two-dimensional bilayer shallow water equations

2015 ◽  
Vol 96 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Nouh Izem ◽  
Mohammed Seaid ◽  
Imad Elmahi ◽  
Mohamed Wakrim
Keyword(s):  
Galerkin Method ◽  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Shallow Water Equations ◽  
Two Dimensional

scholarly journals Multiwavelet Discontinuous Galerkin-Accelerated Exact Linear Part (ELP) Method for the Shallow-Water Equations on the Cubed Sphere

2011 ◽  
Vol 139 (2) ◽  
pp. 457-473 ◽  
Author(s):  
Rick Archibald ◽  
Katherine J. Evans ◽  
John Drake ◽  
James B. White
Keyword(s):  
Galerkin Method ◽  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Shallow Water Equations ◽  
Linear Part ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Cubed Sphere

Abstract In this paper a new approach is presented to increase the time-step size for an explicit discontinuous Galerkin numerical method. The attributes of this approach are demonstrated on standard tests for the shallow-water equations on the sphere. The addition of multiwavelets to the discontinuous Galerkin method, which has the benefit of being scalable, flexible, and conservative, provides a hierarchical scale structure that can be exploited to improve computational efficiency in both the spatial and temporal dimensions. This paper explains how combining a multiwavelet discontinuous Galerkin method with exact-linear-part time evolution schemes, which can remain stable for implicit-sized time steps, can help increase the time-step size for shallow-water equations on the sphere.

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