Space-time SUPG formulation of the shallow-water equations

2010 ◽  
Vol 64 (10-12) ◽  
pp. 1379-1394 ◽  
Author(s):  
Shinsuke Takase ◽  
Kazuo Kashiyama ◽  
Seizo Tanaka ◽  
Tayfun E. Tezduyar
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Space Time ◽  
Supg Formulation

Numerical Model of Natural River Flow by Unstructure Space-Time SE-CE Method

2011 ◽  
Vol 101-102 ◽  
pp. 392-395
Author(s):  
Ji Lun Miao ◽  
Xiao Xin Fei ◽  
Cheng Lin Huang
Keyword(s):  
Numerical Model ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Field Data ◽  
River Flow ◽  
Space Time ◽  
Two Dimensional ◽  
Proposed Model ◽  
Complex Boundaries ◽  
Natural Rivers

A new horizontal two-dimensional mathematic scheme namely space-time Conservation Element and Solution Element (CE-SE) is introduced in this paper. The CE-SE method has some features which space and time are unified and treated on the same footing, both local and global flux are enforced conservation. The proposed model is applied to solve the 2-D shallow water equations in the triangular mesh, and tested by using the field data in Yangzi River. It shows that the hydraulics characters in natural rivers which are with complex boundaries and topography can be well simulated by using this new method.

An adaptive space-time shock capturing method with high order wavelet bases for the system of shallow water equations

2018 ◽  
Vol 28 (12) ◽  
pp. 2842-2861
Author(s):  
Hadi Minbashian ◽  
Hojatollah Adibi ◽  
Mehdi Dehghan
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Degrees Of Freedom ◽  
Adaptive Method ◽  
Space Time ◽  
High Order ◽  
Shock Capturing ◽  
Weak Formulation ◽  
Content Type ◽  
Wavelet Expansions

PurposeThis paper aims to propose an adaptive method for the numerical solution of the shallow water equations (SWEs). The authors provide an arbitrary high-order method using high-order spline wavelets. Furthermore, they use a non-linear shock capturing (SC) diffusion which removes the necessity of post-processing.Design/methodology/approachThe authors use a space-time weak formulation of SWEs which exploits continuous Galerkin (cG) in space and discontinuous Galerkin (dG) in time allowing time stepping, also known as cGdG. Such formulations along with SC term have recently been proved to ensure the stability of fully discrete schemes without scarifying the accuracy. However, the resulting scheme is expensive in terms of number of degrees of freedom (DoFs). By using natural adaptivity of wavelet expansions, the authors devise an adaptive algorithm to reduce the number of DoFs.FindingsThe proposed algorithm uses DoFs in a dynamic way to capture the shocks in all time steps while keeping the representation of approximate solution sparse. The performance of the proposed scheme is shown through some numerical examples.Originality/valueAn incorporation of wavelets for adaptivity in space-time weak formulations applied for SWEs is proposed.

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