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This paper develops high-order well-balanced (WB) energy stable (ES) finite difference schemes for multi-layer (the number of layers $M\geqslant 2$) shallow water equations (SWEs) on both fixed and adaptive moving meshes, extending our…
We propose an unconditionally energy-stable, orthonormality-preserving, component-wise splitting iterative scheme for the Kohn-Sham gradient flow based model in the electronic structure calculation. We first study the scheme discretized in…
We address the question of parameterizing the subgrid scales in simulations of geophysical flows by applying stochastic mode reduction to the one-dimensional stochastically forced shallow water equations. The problem is formulated in…
Shallow free surface flows are often characterized by both subdomains that require high modeling complexity and subdomains that can be sufficiently accurately modeled with low modeling complexity. Moreover, these subdomains may change in…
We present a central differencing scheme for the solution of the shallow water equations with non-flat bottom topography and moving wet-dry fronts. The problem is numerically challenging due to two reasons. First, the non-flat bottom…
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…
In this paper, we introduce a methodology to design genuinely two-dimensional (2D) secondorder path-conservative central-upwind (PCCU) schemes. The scheme studies dam-break with high sediment concentration over abrupt moving topography…
This paper presents a family of spatial discretisations of the nonlinear rotating shallow-water equations that conserve both energy and potential enstrophy. These are based on two-dimensional mixed finite element methods and hence, unlike…
Computational fluid dynamics lies at the heart of many issues in science and engineering, but solving the associated partial differential equations remains computationally demanding. With the rise of quantum computing, new approaches have…
We describe a compatible finite element discretisation for the shallow water equations on the rotating sphere, concentrating on integrating consistent upwind stabilisation into the framework. Although the prognostic variables are velocity…
In this paper, we consider a mass conservation, positivity and energy identical-relation preserving scheme for the Navier-Stokes equations with variable density. Utilizing the square transformation, we first ensure the positivity of the…
We introduce a class of unconditionally energy stable, high order accurate schemes for gradient flows in a very general setting. The new schemes are a high order analogue of the minimizing movements approach for generating a time discrete…
The numerical solution of relativistic hydrodynamics equations in conservative form requires root-finding algorithms that invert the conservative-to-primitive variables map. These algorithms employ the equation of state of the fluid and can…
In this paper, an energy-consistent finite difference scheme for the compressible hydrodynamic and magnetohydrodynamic (MHD) equations is introduced. For the compressible magnetohydrodynamics, an energy-consistent finite difference…
It is shown how various ideas that are well established for the solution of Poisson's equation using plane wave and multigrid methods can be combined with wavelet concepts. The combination of wavelet concepts and multigrid techniques turns…
Hydrodynamic modelling is an important tool for the development of tidal stream energy projects. Many hydrodynamic models incorporate the effect of tidal turbines through an enhanced bottom drag. In this paper we show that although for…
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 work, we design an entropy stable, finite volume approximation for the shallow water magnetohydrodynamics (SWMHD) equations. The method is novel as we design an affordable analytical expression of the numerical interface flux…
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…
We propose a novel model to obtain the subgrid-scale velocity in the context of large-eddy simulation (LES) of particle-laden turbulent flows, to recover accurate particle statistics. In the new wavelet enrichment model, the subgrid-scale…