A vertex-based finite volume method for Laplace operator on triangular grids is proposed in which Dirichlet boundary conditions are implemented weakly. The scheme satisfies a summation-by-parts (SBP) property including boundary conditions which can be used to prove energy stability of the scheme for the heat equation. A Nitsche-type penalty term is proposed which gives improved accuracy. The sc...

This work is devoted to the design of multi-dimensional finite volume schemes for solving transport equations on unstructured grids. In the framework of MUSCL vertex-based methods we construct numerical fluxes such that the local maximum property is guaranteed under an explicit Courant-Friedrichs-Levy condition. The method can be naturally completed by adaptive local mesh refinements and it tur...

This paper discusses the implementation of an explicit density-based solver, based on the central-upwind schemes originally suggested by Kurganov, for the simulation of cavitating bubble dynamic flows. Explicit density based solvers are suited for highly dynamic, violent flows, involving large density ratios, as is rather common in cavitating flows. Moreover, the central-upwind schemes have the...

Solutions of conservation laws satisfy the monotonicity property: the number of local extrema is a non-increasing function of time, and local maximum/minimum values decrease/increase monotonically in time. This paper investigates this property from a numerical standpoint. We introduce a class of fully discrete in space and time, high order accurate, diierenceschemes, called generalized monotone...

The present paper deals with the continuous work of extending the application of a multidimensional-type solution reconstruction and limiting procedure into the finite volume (FV) computation of 2D compressible flows. Based on a MUSCL-type technique, this reconstruction procedure identifies and cures poor connected grids without suffering from loss of accuracy by taking into account geometrical...

Abstract Since its inception, the full Lagrangian meshless smoothed particle hydrodynamics (SPH) has experienced a tremendous enhancement in methodology and impacted range of multi-physics applications science engineering. This review presents concise survey on latest developments achievements SPH method, including: (1) Brief theory fundamental with kernel corrections, (2) The Riemann-based met...

The proposed work concerns the numerical approximations of the shallow-water equations with varying topography. The main objective is to introduce an easy and systematic technique to enforce the well-balance property and to make the scheme able to deal with dry areas. To access such an issue, the derived numerical method is obtained by involving the free surface instead of the water height and ...

In this paper we develop a new technique, called \textit{state redistribution}, that allows the use of explicit time stepping when approximating solutions to hyperbolic conservation laws on embedded boundary grids. State redistribution is postprocessing technique applied after each step or stage base finite volume scheme, using proportional full cells. The idea stabilize cut cells by temporaril...

This paper focuses on the implementation of an accurate meshless scheme for simulation advection–diffusion non-active pollutant in a two-dimensional depth-averaged flow. The flow model includes shallow water system and propagation described by equation with diffusion tensor. mathematical was implemented using method based local radial basis functions. used to numerically evaluate spatial deriva...

In this report, we present parallel solutions of realistic three-dimensional ows obtained on the Intel Paragon, the Cray T3D and the Ibm SP2 MPPs (Massively Parallel Processors). The solver under consideration is a representative subset of an existing industrial code, N3S-MUSCL (a three-dimensional compressible Navier-Stokes solver, see Chargyy3]). It implements a mixed nite element//nite volum...