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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…
We present a first order scheme based on a staggered grid for the shallow water equations with topography in two space dimensions, which enjoys several properties: positivity of the water height, preservation of constant states, and weak…
The present work focuses on the numerical approximation of the weak solutions of the shallow water model over a non-flat topography. In particular, we pay close attention to steady solutions with nonzero velocity. The goal of this work is…
This note aims at demonstrating the advantage of moving-water well-balanced schemes over still-water well-balanced schemes for the shallow water equations. We concentrate on numerical examples with solutions near a moving-water equilibrium.…
In this work, using a unified framework consisting of third-order accurate discontinuous Galerkin schemes, we perform a comparison between five different numerical approaches to the free-surface shallow flow simulation on bottom steps.…
This paper is concerned with the construction of high order schemes on irregular grids for balance laws, including a discussion of an a-posteriori error indicator based on the numerical entropy production. We also impose well-balancing on…
In ordinary turbulence research it has been a long standing tradition to solve the equations in spectral space giving the best possible accuracy. This is indeed a natural choice for incompressible problems with periodic boundaries, but it…
The present work is devoted to the derivation of a fully well-balanced and positivepreserving numerical scheme for the shallow water equations with Coriolis force. The first main issue consists in preserving all the steady states, including…
In this paper, we study a numerical artifact of solving the nonlinear shallow water equations with a discontinuous bottom topography. For various first-order schemes, the numerical solution of the momentum will form a spurious spike at the…
First-order hydrostatic reconstruction (HR) schemes for shallow water equations are highly diffusive whereas high-order schemes can produce entropy-violating solutions. Our goal is to develop a flux correction with maximum antidiffusive…
We formulate a general criterion for the exact preservation of the "lake at rest" solution in general mesh-based and meshless numerical schemes for the strong form of the shallow-water equations with bottom topography. The main idea is a…
Many numerical schemes for hyperbolic systems require a piecewise polynomial reconstruction of the cell averaged values, and to simulate perturbed steady states accurately we require a so called 'well balanced' reconstruction scheme. For…
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…
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,…
The aim of this paper is to study a whole class of first order differential inclusions, which fit into the framework of perturbed sweeping process by uniformly prox-regular sets. After obtaining well-posedness results, we propose a…
The efficiency of several first-order numerical schemes for two-layer shallow water equations are evaluated in this paper by considering different eigenvalue solutions. Specifically, the accuracy and computational cost of numerical,…
Numerical simulations for flow and transport in subsurface porous media often prove computationally prohibitive due to property data availability at multiple spatial scales that can vary by orders of magnitude. A number of model order…
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…
In this work, we propose a second-order accurate scheme for shallow water equations in general covariant coordinates over manifolds. In particular, the covariant parametrization in general covariant coordinates is induced by the metric…