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We introduce a continuous Galerkin finite element discretization of the non-hydrostatic Boussinesq approximation of the Navier-Stokes equations, suitable for various applications such as coastal ocean dynamics and ice-ocean interactions,…
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.…
We consider a class of time dependent second order partial differential equations governed by a decaying entropy. The solution usually corresponds to a density distribution, hence positivity (non-negativity) is expected. This class of…
This article proposes entropy stable discontinuous Galerkin schemes (DG) for two-fluid relativistic plasma flow equations. These equations couple the flow of relativistic fluids via electromagnetic quantities evolved using Maxwell's…
We formulate a coupled surface/subsurface flow model that relies on hydrostatic equations with free surface in the free flow domain and on the Darcy model in the subsurface part. The model is discretized using the local discontinuous…
Fluid discontinuities, such as shock fronts and vortex sheets, can reflect waves and become unstable to corrugation. Analytical calculations of these phenomena are tractable in the simplest cases only, while their numerical simulations are…
We develop a discretely entropy-stable line-based discontinuous Galerkin method for hyperbolic conservation laws based on a flux differencing technique. By using standard entropy-stable and entropy-conservative numerical flux functions,…
In this paper, we develop hybridized discontinuous Galerkin (HDG) methods for poroelastic wave equations. We first rewrite the governing equations to a first-order symmetric hyperbolic system in order to use dual mixed formulations for…
In this study, we consider the simulation of subsurface flow and solute transport processes in the stationary limit. In the convection-dominant case, the numerical solution of the transport problem may exhibit non-physical diffusion and…
We consider the Shallow Water equations in the supercritical and subcritical cases in one space variable,posed in a finite spatial interval with characteristic boundary conditions at the endpoints, which, as is well known, are…
Element Method. The Finite Volume Method guarantees local and global mass conservation. A property not satisfied by the Finite Volume Method. On the down side, the Finite Volume Method requires non trivial modifications to attain high order…
We present and analyze a discontinuous Galerkin method for the numerical modeling of the non-linear fully-coupled thermo-hydro-mechanic problem. We propose a high-order symmetric weighted interior penalty scheme that supports general…
We propose a new parallel Discontinuous Galerkin method for the approximation of hyperbolic systems of conservation laws. The method remains stable with large time steps, while keeping the complexity of an explicit scheme: it does not…
We analyze an iterative coupling of mixed and discontinuous Galerkin methods for numerical modelling of coupled flow and mechanical deformation in porous media. The iteration is based on an optimized fixed-stress split along with a…
We assess the ability of three different approaches based on high-order discontinuous Galerkin methods to simulate under-resolved turbulent flows. The capabilities of the mass conserving mixed stress method as structure resolving large eddy…
A novel wetting and drying treatment for second-order Runge-Kutta discontinuous Galerkin (RKDG2) methods solving the non-linear shallow water equations is proposed. It is developed for general conforming two-dimensional triangular meshes…
We present the extension of an efficient and highly parallelisable framework for incompressible fluid flow simulations to viscoplastic fluids. The system is governed by incompressible conservation of mass, the Cauchy momentum equation and a…
In this paper, we develop an adaptive multiresolution discontinuous Galerkin (DG) scheme for scalar hyperbolic conservation laws in multidimensions. Compared with previous work for linear hyperbolic equations \cite{guo2016transport,…
This paper presents a new and unified approach to the derivation and analysis of many existing, as well as new discontinuous Galerkin methods for linear elasticity problems. The analysis is based on a unified discrete formulation for the…
This paper proposes a novel computational framework for the solution of geometrically parametrised flow problems governed by the Stokes equation. The proposed method uses a high-order hybridisable discontinuous Galerkin formulation and the…