An adaptive well-balanced positivity preserving scheme on quadtree grids for shallow water equations

11/27/2019
by   Mohammad A. Ghazizadeh, et al.
0

We present an adaptive well-balanced positivity preserving scheme on quadtree grids for shallow water equations. The use of quadtree grids results in a robust, efficient and highly accurate numerical method. The quadtree model is developed based on the well-balanced positivity preserving central-upwind scheme proposed in [ A. Kurganov and G. Petrova, Commun. Math. Sci., 5 (2007), pp. 133–160]. The designed scheme is well-balanced in the sense that it is capable of exactly preserving "lake-at-rest" steady states. In order to achieve this as well as to preserve positivity of water depth, a continuous piecewise bi-linear interpolation of the bottom topography function is utilized. Local gradients are examined to determine new seeding points in grid refinement for the next timestep. Numerical examples demonstrate the promising performance of the central-upwind quadtree scheme.

READ FULL TEXT

Authors

page 15

page 17

page 18

08/03/2020

An adaptive central-upwind scheme on quadtree grids for variable density shallow water equations

Minimizing computational cost is one of the major challenges in the mode...
11/21/2019

A Well-Balanced Central-Upwind Scheme for the Thermal Rotating Shallow Water Equations

We develop a well-balanced central-upwind scheme for rotating shallow wa...
01/25/2022

Adaptive Central-Upwind Scheme on Triangular Grids for the Shallow Water Model with variable density

In this paper, we construct a robust adaptive central-upwind scheme on u...
11/16/2020

Steady States and Well-balanced Schemes for Shallow Water Moment Equations with Topography

In this paper, we investigate steady states of shallow water moment equa...
04/22/2021

Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Two-Dimensional Shallow Water Equations

Stochastic Galerkin formulations of the two-dimensional shallow water sy...
08/18/2020

Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Shallow Water Equations

A stochastic Galerkin formulation for a stochastic system of balanced or...
11/12/2020

Adaptive Central-Upwind Scheme on Triangular Grids for the Saint-Venant System

In this work, we develop a robust adaptive well-balanced and positivity-...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.