Related papers: An IMEX-DG solver for atmospheric dynamics simulat…

This work concerns the numerical approximation of a multicomponent compressible Euler system for a fluid mixture in multiple space dimensions on unstructured meshes with a high-order discontinuous Galerkin spectral element method (DGSEM).…

While many methods exist to discretize nonlinear time-dependent partial differential equations (PDEs), the rigorous estimation and adaptive control of their discretization errors remains challenging. In this paper, we present a methodology…

This article studies a dirichlet boundary value problem for singularly perturbed time delay convection diffusion equation with degenerate coefficient. A priori explicit bounds are established on the solution and its derivatives. For…

The nonhydrostatic High Order Method Modeling Environment (HOMME-NH) atmospheric dynamical core supports acoustic waves that propagate significantly faster than the advective wind speed, thus greatly limiting the timestep size that can be…

In this work a non-conservative balance law formulation is considered that encompasses the rotating, compressible Euler equations for dry atmospheric flows. We develop a semi-discretely entropy stable discontinuous Galerkin method on…

In this work we consider Runge-Kutta discontinuous Galerkin methods (RKDG) for the solution of hyperbolic equations enabling high order discretization in space and time. We aim at an efficient implementation of DG for Euler equations on…

In convection-dominated flows, robustness of the spatial discretisation is a key property. While Interior Penalty Galerkin (IPG) methods already proved efficient in the situation of large mesh Peclet numbers, Arbitrary Lagrangian-Eulerian…

This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution by using…

Euler--Euler or volume-averaged Navier--Stokes equations are used in various applications to model systems with two or more interpenetrating phases. Each fluid obeys its own momentum and mass equations, and the phases are typically coupled…

For linear transport and radiative heat transfer equations with random inputs, we develop new generalized polynomial chaos based Asymptotic-Preserving stochastic Galerkin schemes that allow efficient computation for the problems that…

As a first step towards the numerical analysis of the stochastic primitive equations of the atmosphere and oceans, we study their time discretization by an implicit Euler scheme. From deterministic viewpoint the 3D Primitive Equations are…

We study the slightly compressible Darcy-Forchheimer equations modeling gas flow in porous media, particularly in applications related to combustion processes. The equations are discretized in time using the backward Euler method and in…

We present an accurate and efficient discretization approach for the adaptive discretization of typical model equations employed in numerical weather prediction. A semi-Lagrangian approach is combined with the TR-BDF2 semi-implicit time…

High-order Discontinuous Galerkin Spectral Element Methods (DGSEM) provide excellent accuracy for complex flow simulations, but their computational cost increases sharply with higher polynomial orders. %that provide very accurate solutions.…

We develop structure-preserving numerical methods for the compressible Euler equations, employing potential temperature as a prognostic variable. We construct three numerical fluxes designed to ensure the conservation of entropy and total…

In this report, we propose a collection of methods to make such an approach possible for Euler equations in one and two dimensions. We propose an explicit single-step ALE DG scheme for hyperbolic conservation laws. The scheme considerably…

We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…

In this paper, we develop a discrete unified gas kinetic scheme (DUGKS) for general nonlinear convection-diffusion equation (NCDE), and show that the NCDE can be recovered correctly from the present model through the Chapman-Enskog…

We present a discontinuous Galerkin method for moist atmospheric dynamics, with and without warm rain. By considering a combined density for water vapour and cloud water, we avoid the need to model and compute a source term for…

The Stokes equations play an important role in the incompressible flow simulation. In this paper, a novel divergence-free parametric mixed finite element method is proposed for solving three-dimensional Stokes equations on domains with…