Related papers: A Study of Improved Limiter Formulations for Secon…
This work primarily focuses on the study of three gradient reconstruction techniques applied to the calculation of viscous terms in a cell-centered, finite volume formulation for general unstructured grids. The work also addresses different…
In the context of the cell centered finite volume approach, care must be taken when performing the reconstruction of property gradients at cell interfaces. The present work analyzes three different gradient reconstruction procedures, using…
In this article, we propose a finite volume limiter function for a reconstruction on the three-point stencil. Compared to classical limiter functions in the MUSCL framework, which yield $2^{\text{nd}}$-order accuracy, the new limiter is…
We propose a new curl-free and thermodynamically compatible finite volume scheme on Voronoi grids to solve compressible heat conducting flows written in first-order hyperbolic form. The approach is based on the definition of compatible…
This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing…
In this paper we extend the recently developed third-order limiter function $H_{3\text{L}}^{(c)}$ [J. Sci. Comput., (2016), 68(2), pp.~624--652] to make it applicable for more elaborate test cases in the context of finite volume schemes.…
Most slope limiter functions in high-resolution finite volume methods to solve hyperbolic conservation laws are designed assuming one-dimensional uniform grids, and they are also used to compute slope limiters in computations on non-uniform…
We propose a new unstructured numerical subgrid method for solving the shallow water equations using a finite volume method with enhanced bathymetry resolution. The method employs an unstructured triangular mesh with support for…
This paper extends the author's previous two-dimensional work with Ou and LeVeque to high-resolution finite volume modeling of systems of fluids and poroelastic media in three dimensions, using logically rectangular mapped grids. A method…
We present the implementation and validation of an immersed boundary volume penalization method in the computational fluid dynamics solver CODA (from ONERA, DLR, and Airbus). Our goal is to model and simulate turbulent fluid flows in…
We present a generalized form of open boundary conditions, and an associated numerical algorithm, for simulating incompressible flows involving open or outflow boundaries. The generalized form represents a family of open boundary…
Conventional mathematical models for simulating incompressible fluid flow problems are based on the Navier-Stokes equations expressed in terms of pressure and velocity. In this context, pressure-velocity coupling is a key issue, and…
This paper addresses the problem of obtaining low-order models of fluid flows for the purpose of designing robust feedback controllers. This is challenging since whilst many flows are governed by a set of nonlinear, partial…
This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma…
A third-order weighted essentially non-oscillatory compact least-squares scheme is developed for the finite volume method on structured curvilinear non-uniform grids. The proposed scheme features compact least-squares reconstruction with…
We propose a simple modification of standard WENO finite volume methods for Cartesian grids, which retains the full spatial order of accuracy of the one-dimensional discretization when applied to nonlinear multidimensional systems of…
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…
Higher-order numerical methods are used to find accurate numerical solutions to hyperbolic partial differential equations and equations of transport type. Limiting is required to either converge to the correct type of solution or to adhere…
Non-orthogonality errors in unstructured Finite Volume methods for simulating incompressible two-phase flows may break the force-balanced discretization. We show that applying the same explicit non-orthogonality correction for all gradient…
Weighted essentially non-oscillatory (WENO) and finite volume (FV) methods employ different philosophies in their way to perform limiting. We show that a generalized view on limiter functions, which considers a two-dimensional, rather than…