A Well-Balanced SPH-ALE Scheme for Shallow Water Applications

Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG[Abstract] In this work, a new discretization of the source term of the shallow water equations with non-flat bottom geometry is proposed to obtain a well-balanced scheme. A Smoothed Particle Hydrodynamics Arbitrary Lagrangian-Eulerian formulation based on Riemann solvers is presented to solve the SWE. Moving-Least Squares approximations are used to compute high-order reconstructions of the numerical fluxes and, stability is achieved using the a posteriori MOOD paradigm. Several benchmark 1D and 2D numerical problems are considered to test and validate the properties and behavior of the presented schemes.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This work has been partially supported by FEDER funds of the European Union, Grant #RTI2018-093366-B-I00 of the Ministerio de Ciencia, Innovación y Universidades of the Spanish Government and by the Consellería de Educación e Ordenación Universitaria of the Xunta de Galicia (grant# ED431C 2018/41). Luis Ramírez also acknowledges the funding provided by the Xunta de Galicia through the program Axudas para a mellora, creación, recon~ecemento e estruturación de agrupacións estratéxicas do Sistema universitario de Galicia (reference # ED431E 2018/11)Xunta de Galicia; ED431C 2018/41Xunta de Galicia; ED431E 2018/1

a posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equations

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a posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equations

We propose a new family of finite volume high-accurate numerical schemes devoted to solve one-dimensional steady-state hyperbolic systems. High-accuracy (up to the sixth-order presently) is achieved thanks to polynomial reconstructions while stability is provided with an a posteriori MOOD method which control the cell polynomial degree for eliminating non-physical oscillations in the vicinity of discontinuities. Such a procedure demands the determination of a chain detector to discriminate between troubled and valid cells, a cascade of polynomial degrees to be successively tested when oscillations are detected, and a parachute scheme corresponding to the last, viscous, and robust scheme of the cascade. Experimented on linear, Burgers', and Euler equations, we demonstrate that the schemes manage to retrieve smooth solutions with optimal order of accuracy but also irregular solutions without spurious oscillations