Related papers: A simple HLLE-type scheme for all Mach number flow…
An asymptotic preserving and energy stable scheme for the barotropic Euler system under the low Mach number scaling is designed and analysed. A velocity shift proportional to the pressure gradient is introduced in the convective fluxes,…
Fully compressible magnetohydrodynamic (MHD) simulations are a fundamental tool for investigating the role of dynamo amplification in the generation of magnetic fields in deep convective layers of stars. The flows that arise in such…
The majority of coastal flows are characterized by turbulence, rendering the application of shallow water equations an inadequate approach for their accurate description. This paper presents a theory for characterizing accelerated coastal…
The 1-D Two-Fluid Model (TFM) promises a powerful and computationally cheap platform for simulating multi-fluid flow phenomena. However, runaway Kelvin-Helmholtz instabilities plagued previous approaches, necessitating aphysical…
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 present an explicit scheme for a two-dimensional multilayer shallow water model with density stratification, for general meshes and collocated variables. The proposed strategy is based on a regularized model where the transport velocity…
We propose novel less diffusive schemes for conservative one- and two-dimensional hyperbolic systems of nonlinear partial differential equations (PDEs). The main challenges in the development of accurate and robust numerical methods for the…
The Holomorphic Embedding Load-Flow Method (HELM) was recently introduced as a novel technique to constructively solve the power-flow equations in power grids, based on advanced complex analysis. In this paper, the theoretical foundations…
In the last decades, more or less complex physically-based hydrological models, have been developed to solve the shallow water equations or their approximations using various numerical methods. The MacCormack method was developed for…
We describe a numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference scheme on an Eulerian grid, called the Total Variation Diminishing (TVD) scheme, which is a…
The capability to accurately predict flood flows via numerical simulations is a key component of contemporary flood risk management practice. However, modern flood models lack the capacity to accurately model flow interactions with linear…
This paper introduces multidimensional algorithms for simulating multiphase flows, leveraging the wave structure of the Euler equations in characteristic space and the physical properties of variables in physical space. The algorithm…
In this paper we present results from a series of hydrodynamical tests aimed at validating the performance of a smoothed particle hydrodynamics (SPH) formulation in which gradients are derived from an integral approach. We specifically…
Accurate high-speed flow simulations of practical interest require numerical methods with high-resolution properties. In this paper, we present an extension and demonstration of the high-accuracy Gradient-based reconstruction and…
In this paper, we propose a simple hybrid WENO scheme to increase computational efficiency and decrease numerical dissipation. Based on the characteristic-wise approach, the scheme switches the numerical flux of each characteristic…
We introduce a low Mach number model for moist atmospheric flows that accurately incorporates reversible moist processes in flows whose features of interest occur on advective rather than acoustic time scales. Total water is used as a…
A linear stability analysis is performed on a tilted parallel wake in a strongly stratified fluid at low Reynolds numbers. A particular emphasis of the present study is given to the understanding of the low-Froude-number mode observed by…
Here, we provide a theoretical framework revealing that a steady compression ramp flow must have the minimal dissipation of kinetic energy, and can be demonstrated using the least action principle. For a given inflow Mach number $M_{0}$ and…
Developing high-order numerical schemes for two-phase flow in porous media that preserve key physical properties remains a significant challenge in numerical analysis. In this article, we propose a general framework to construct fully…
The shear shallow water model is an extension of the classical shallow water model to include the effects of vertical shear. It is a system of six non-linear hyperbolic PDE with non-conservative products. We develop a high-order entropy…