Treffer: A well-balanced second-order finite volume approximation for a coupled system of granular flow

Title:
A well-balanced second-order finite volume approximation for a coupled system of granular flow
Authors:
Aggarwal, Aekta, D., Veerappa Gowda G., K., Sudarshan Kumar
Source:
Journal of Computational Physics. 510:113068
Publication Status:
Preprint
Publisher Information:
Elsevier BV, 2023.
Publication Year:
2023
Subject Terms:
Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs, sandpile, balance laws, Finite volume methods for initial value and initial-boundary value problems involving PDEs, well-balanced schemes, FOS: Mathematics, Hamilton Jacobi equations, Finite volume methods applied to problems in fluid mechanics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, discontinuous flux
Document Type:
Fachzeitschrift Article
File Description:
application/xml
Language:
English
ISSN:
0021-9991
DOI:
10.1016/j.jcp.2024.113068
DOI:
10.2139/ssrn.4664973
DOI:
10.48550/arxiv.2310.13971
Access URL:
http://arxiv.org/abs/2310.13971
https://zbmath.org/8021034
https://doi.org/10.1016/j.jcp.2024.113068
Rights:
Elsevier TDM
CC BY
Accession Number:
edsair.doi.dedup.....0adfb4d5a9c3839e5ed41c47c3836d7d
Database:
OpenAIRE

Weitere Informationen

A well-balanced second-order finite volume scheme is proposed and analyzed for a 2 X 2 system of non-linear partial differential equations which describes the dynamics of growing sandpiles created by a vertical source on a flat, bounded rectangular table in multiple dimensions. To derive a second-order scheme, we combine a MUSCL type spatial reconstruction with strong stability preserving Runge-Kutta time stepping method. The resulting scheme is ensured to be well-balanced through a modified limiting approach that allows the scheme to reduce to well-balanced first-order scheme near the steady state while maintaining the second-order accuracy away from it. The well-balanced property of the scheme is proven analytically in one dimension and demonstrated numerically in two dimensions. Additionally, numerical experiments reveal that the second-order scheme reduces finite time oscillations, takes fewer time iterations for achieving the steady state and gives sharper resolutions of the physical structure of the sandpile, as compared to the existing first-order schemes of the literature.