Related papers: A Numerical Technique for Coupling the Momentum an…
We present compact semi-implicit finite difference schemes on structured grids for numerical solutions of the advection by an external velocity and by a speed in normal direction that are applicable in level set methods. The most involved…
We propose and analyze a new method for the unsteady incompressible magnetohydrodynamics equations on convex domains with hybrid approximations of both vector-valued and scalar-valued fields. The proposed method is convection-semirobust,…
A finite element method for the numerical solution of the anisotropic Navier-Stokes equations in shallow domain is presented. This method take into account aspect ratio in the hydrostatic approximation of the Navier-Stokes equations…
We present a parametric family of semi-implicit second order accurate numerical methods for non-conservative and conservative advection equation for which the numerical solutions can be obtained in a fixed number of forward and backward…
Analysing two-dimensional shallow water equations with idealised bottom topographies have many applications in the atmospheric and oceanic sciences; however, restrictive flow pattern assumptions have been made to achieve explicit solutions.…
Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system of PDEs, the so-called moment system. This calls for tailored model order reduction techniques…
Surface-subsurface flow models for hydrological applications solve a coupled multiphysics problem. This usually consists of some form of the Richards and shallow water equations. A typical setup couples these two nonlinear partial…
We derive and analyze a broad class of finite element methods for numerically simulating the stationary, low Reynolds number flow of concentrated mixtures of several distinct chemical species in a common thermodynamic phase. The underlying…
This paper presents a conforming finite element semi-discretization of the streamfunction form of the one-layer unsteady quasi-geostrophic equations, which are a commonly used model for large-scale wind-driven ocean circulation. We derive…
Two effective methods for writing the dynamical equations for non-holonomic systems are illustrated. They are based on the two types of representation of the constraints: by parametric equations or by implicit equations. They can be applied…
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…
We present a novel asymptotic-preserving semi-implicit finite element method for weakly compressible and incompressible flows based on compatible finite element spaces. The momentum is sought in an $H(\mathrm{div})$-conforming space,…
A fully coupled implicit finite-volume algorithm for incompressible viscoelastic interfacial flows is proposed, whereby the viscoelasticity of the flow is described by an upper-convected Maxwell constitutive model, including limited…
We propose a new mixed finite element method for the three-dimensional steady magnetohydrodynamic (MHD) kinematics equations for which the velocity of the fluid is given. Although prescribing the velocity field leads to a simpler model than…
Magnetohydrostatic models of the solar atmosphere are often based on idealized analytic solutions because the underlying equations are too difficult to solve in full generality. Numerical approaches, too, are often limited in scope and have…
In this paper a new semi-implicit relaxation scheme for the simulation of multi-scale hyperbolic conservation laws based on a Jin-Xin relaxation approach is presented. It is based on the splitting of the flux function into two or more…
In this study, a novel semi-implicit second-order temporal scheme combined with the finite element method for space discretization is proposed to solve the coupled system of infiltration and solute transport in unsaturated porous media. The…
We present novel coupling schemes for partitioned multi-physics simulation that combine four important aspects for strongly coupled problems: implicit coupling per time step, fast and robust acceleration of the corresponding iterative…
This study concerns numerical methods for efficiently solving the Richards equation where different weak formulations and computational techniques are analyzed. The spatial discretizations are based on standard or mixed finite element…
We introduce novel high order well-balanced finite volume methods for the full compressible Euler system with gravity source term. They require no a priori knowledge of the hydrostatic solution which is to be well-balanced and are not…