A Well-Balanced SPH-ALE Scheme for Shallow Water Applications
Alberto Prieto-Arranz, Luis Ramírez, Iván Couceiro, Ignasi Colominas, Xesús Nogueira
Abstract
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.
Topics & Concepts
MathematicsDiscretizationShallow water equationsA priori and a posterioriRiemann solverBenchmark (surveying)Applied mathematicsStability (learning theory)Smoothed-particle hydrodynamicsLagrangianWork (physics)Eulerian pathRiemann hypothesisWaves and shallow waterMathematical analysisMechanicsComputer scienceGeologyFinite volume methodEpistemologyPhysicsMechanical engineeringGeodesyOceanographyPhilosophyMachine learningEngineeringFluid Dynamics Simulations and InteractionsLattice Boltzmann Simulation StudiesComputational Fluid Dynamics and Aerodynamics