Related papers: Arbitrary Order Energy and Enstrophy Conserving Fi…
This paper explores Tadmor's minimum entropy principle for the relativistic hydrodynamics (RHD) equations and incorporates this principle into the design of robust high-order discontinuous Galerkin (DG) and finite volume schemes for RHD on…
We design consistent discontinuous Galerkin finite element schemes for the approximation of a quasi-incompressible two phase flow model of Allen-Cahn/Cahn-Hilliard/Navier-Stokes-Korteweg type which allows for phase transitions. We show that…
We present and discuss three discontinuous Galerkin (dG) discretizations for the anisotropic heat conduction equation on non-aligned cylindrical grids. Our most favourable scheme relies on a self-adjoint local dG (LDG) discretization of the…
A computationally accurate and efficient numerical method under a unified framework is crucial to various multi-scale scientific and engineering problems. So far, many numerical methods have encountered various challenges in efficiently…
A discontinuous Galerkin (DG) method suitable for large-scale astrophysical simulations on Cartesian meshes as well as arbitrary static and moving Voronoi meshes is presented. Most major astrophysical fluid dynamics codes use a finite…
In this paper, we present an entropy-stable Gauss collocation discontinuous Galerkin (DG) method on 3D curvilinear meshes for the GLM-MHD equations: the single-fluid magneto-hydrodynamics (MHD) equations with a generalized Lagrange…
Discontinuous Galerkin (DG) methods are promising high order discretizations for unsteady compressible flows. Here, we focus on Numerical Weather Prediction (NWP). These flows are characterized by a fine resolution in $z$-direction and low…
This paper presents a novel structure-preserving scheme for Euler equations, focusing on the numerical conservation of entropy and kinetic energy. Explicit flux functions engineered to conserve entropy are introduced within the…
This work examines the distributed optimal control of generalized Oseen equations with non-constant viscosity. We propose and analyze a new conforming augmented mixed finite element method and a Discontinuous Galerkin (DG) method for the…
For the general class of residual distribution (RD) schemes, including many finite element (such as continuous/discontinuous Galerkin) and flux reconstruction methods, an approach to construct entropy conservative/ dissipative…
This paper focuses on the numerical approximation of the linearized shallow water equations using hybridizable discontinuous Galerkin (HDG) methods, leveraging the Hamiltonian structure of the evolution system. First, we propose an…
A direct discontinuous Galerkin (DDG) finite element method is developed for solving fractional convection-diffusion and Schr\"{o}dinger type equations with a fractional Laplacian operator of order $\alpha$ $(1<\alpha<2)$. The fractional…
This work presents a novel formulation and numerical strategy for the simulation of geometrically nonlinear structures. First, a non-canonical Hamiltonian (Poisson) formulation is introduced by including the dynamics of the stress tensor.…
A new high order accurate staggered semi-implicit space-time discontinuous Galerkin (DG) method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space dimensions. The staggered DG…
We propose a second-order accurate semi-implicit and well-balanced finite volume scheme for the equations of ideal magnetohydrodynamics (MHD) including gravitational source terms. The scheme treats all terms associated with the acoustic…
Numerical simulation of the spherically symmetric Einstein--Euler (EE) system faces severe challenges due to the stringent physical admissibility constraints of relativistic fluids and the geometric singularities inherent in metric…
An energy preserving reduced order model is developed for two dimensional nonlinear Schr\"odinger equation (NLSE) with plane wave solutions and with an external potential. The NLSE is discretized in space by the symmetric interior penalty…
This paper applies a discontinuous Galerkin finite element method to the Kelvin-Voigt viscoelastic fluid motion equations when the forcing function is in $L^\infty({\bf L}^2)$-space. Optimal a priori error estimates in $L^\infty({\bf…
The construction of discontinuous Galerkin (DG) methods for the compressible Euler or Navier-Stokes equations (NSE) includes the approximation of non-linear flux terms in the volume integrals. The terms can lead to aliasing and stability…
Numerical simulations of compressible real-fluid flows are notoriously plagued by spurious pressure oscillations arising in regions of abrupt flow variations. As a possible remedy, several numerical formulations enforce the pressure…