Well-Balanced Discontinuous Galerkin Method for Shallow Water Equations with Constant Subtraction Techniques on Unstructured Meshes

2019 ◽  
Vol 81 (3) ◽  
pp. 2115-2131
Author(s):  
Huijing Du ◽  
Yingjie Liu ◽  
Yuan Liu ◽  
Zhiliang Xu
Keyword(s):  
Galerkin Method ◽  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Shallow Water Equations ◽  
Unstructured Meshes

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.

scholarly journals A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates

2008 ◽  
Vol 227 (24) ◽  
pp. 10226-10242 ◽  
Author(s):  
Matthias Läuter ◽  
Francis X. Giraldo ◽  
Dörthe Handorf ◽  
Klaus Dethloff
Keyword(s):  
Galerkin Method ◽  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Shallow Water Equations
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