A well-balanced moving mesh discontinuous Galerkin method for the Ripa model on triangular meshes

05/29/2022
by   Weizhang Huang, et al.
0

A well-balanced moving mesh discontinuous Galerkin (DG) method is proposed for the numerical solution of the Ripa model – a generalization of the shallow water equations that accounts for effects of water temperature variations. Thermodynamic processes are important particularly in the upper layers of the ocean where the variations of sea surface temperature play a fundamental role in climate change. The well-balance property which requires numerical schemes to preserve the lake-at-rest steady state is crucial to the simulation of perturbation waves over that steady state such as waves on a lake or tsunami waves in the deep ocean. To ensure the well-balance, positivity-preserving, and high-order properties, a DG-interpolation scheme (with or without scaling positivity-preserving limiter) and special treatments pertaining to the Ripa model are employed in the transfer of both the flow variables and bottom topography from the old mesh to the new one and in the TVB limiting process. Mesh adaptivity is realized using an MMPDE moving mesh approach and a metric tensor based on an equilibrium variable and water depth. A motivation is to adapt the mesh according to both the perturbations of the lake-at-rest steady state and the water depth distribution (bottom structure). Numerical examples in one and two dimensions are presented to demonstrate the well-balance, high-order accuracy, and positivity-preserving properties of the method and its ability to capture small perturbations of the lake-at-rest steady state.

READ FULL TEXT

page 16

page 20

page 30

page 31

page 32

research
06/26/2020

A high-order well-balanced positivity-preserving moving mesh DG method for the shallow water equations with non-flat bottom topography

A rezoning-type adaptive moving mesh discontinuous Galerkin method is pr...
research
10/04/2022

A numerical model preserving nontrivial steady-state solutions for predicting waves run-up on coastal areas

In this study, a numerical model preserving a class of nontrivial steady...
research
08/25/2020

A well-balanced positivity-preserving quasi-Lagrange moving mesh DG method for the shallow water equations

A high-order, well-balanced, positivity-preserving quasi-Lagrange moving...
research
07/19/2023

Novel well-balanced continuous interior penalty stabilizations

In this work, in a monodimensional setting, the high order accuracy and ...
research
05/26/2022

Arbitrary High Order WENO Finite Volume Scheme with Flux Globalization for Moving Equilibria Preservation

In the context of preserving stationary states, e.g. lake at rest and mo...

Please sign up or login with your details

Forgot password? Click here to reset