Related papers: A high-order, fully well-balanced, unconditionally…
We develop a two-dimensional high-order numerical scheme that exactly preserves and captures the moving steady states of the shallow water equations with topography or Manning friction. The high-order accuracy relies on a suitable…
High order finite volume schemes for conservation laws are very useful in applications, due to their ability to compute accurate solutions on quite coarse meshes and with very few restrictions on the kind of cells employed in the…
Preserving scalar boundedness is important for numerical schemes used in turbulent compressible multi-component flow simulations to prevent unphysical results and unstable simulations. However, ensuring scalar boundedness for high-order,…
This paper develops high-order accurate, well-balanced (WB), and positivity-preserving (PP) finite volume schemes for shallow water equations on adaptive moving structured meshes. The mesh movement poses new challenges in maintaining the WB…
Recent scientific studies have suggested that, in certain physical configurations, the time-dependent behavior of earthquake rupture and seafloor (bathymetry) motion can leave observable near-field signatures in tsunami wave generation and…
Shallow water moment equations are reduced-order models for free-surface flows that allow to represent vertical variations of the velocity profile at the expense of additional evolution equations for a number of additional variables, so…
In the present article we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension combined with appropriate predictor-corrector method to achieve higher resolution. The underlying finite…
The development of a set of high-order accurate finite-volume formulations for evaluation of the pressure gradient force in layered ocean models is described. A pair of new schemes are presented, both based on an integration of the contact…
A high-order well-balanced scheme for the Euler equations with gravitation is presented. The scheme is able to preserve a spatially high-order accurate discrete representation of a large class of hydrostatic equilibria. It is based on a…
High-speed turbulent flows are encountered in most space-related applications (including exploration, tourism and defense fields) and represent a subject of growing interest in the last decades. A major challenge in performing high-fidelity…
We are interested in simulating blood flow in arteries with variable elasticity with a one dimensional model. We present a well-balanced finite volume scheme based on the recent developments in shallow water equations context. We thus get a…
In this work, we develop a new hydrostatic reconstruction procedure to construct well-balanced schemes for one and multilayer shallow water flows, including wetting and drying. Initially, we derive the method for a path-conservative finite…
In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual…
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…
Our goal was to develop a robust algorithm for numerical simulation of one-dimensional shallow-water flow in a complex multiply-connected channel network with arbitrary geometry and variable topography. We apply a central-upwind scheme with…
We are interested in simulating blood flow in arteries with a one dimensional model. Thanks to recent developments in the analysis of hyperbolic system of conservation laws (in the Saint-Venant/ shallow water equations context) we will…
We present a high-order method for flow simulation on unstructured curved nonconforming sliding meshes. This method utilizes dynamic transfinite mortar elements to exchange flow information between the two sides of a sliding interface. The…
Finite volume schemes for hyperbolic balance laws require a piecewise polynomial reconstruction of the cell averaged values, and a reconstruction is termed `well-balanced' if it is able to simulate steady states at higher order than time…
We propose high-order well-balanced finite-volume schemes for a broad class of hydrodynamic systems with attractive-repulsive interaction forces and linear and nonlinear damping. Our schemes are suitable for free energies containing…
High order algorithms have emerged in numerical astrophysics as a promising avenue to reduce truncation error (proportional to a power of the linear resolution $\Delta x$) with only a moderate increase to computational expense. Significant…