A spectral-element framework is presented for the simulation of subsonic compressible high-Reynolds-number flows. The focus of the work is maximizing the efficiency of the computational schemes to enable unsteady simulations with a large number of spatial and temporal degrees of freedom. A collocation scheme is combined with optimized computational kernels to provide a residual evaluation with ...

Positivity-preserving discontinuous Galerkin (DG) methods for solving hyperbolic 5 conservation laws have been extensively studied in the last several years. But nearly all the devel6 oped schemes are coupled with explicit time discretizations. Explicit discretizations suffer from the 7 constraint for the Courant-Friedrichs-Levis (CFL) number. This makes explicit methods impractical 8 for probl...

Trefftz methods are high-order Galerkin schemes in which all discrete functions elementwise solution of the PDE to be approximated. They viable only when is linear and its coefficients piecewise-constant. We introduce a “quasi-Trefftz” discontinuous (DG) method for discretisation acoustic wave equation with piecewise-smooth material parameters: approximate solutions. show that new enjoys same e...

In the field of laser generated high energy density physics, hydrodynamics is a very popular approach to describe the created plasma. In the present work, we treat the energy conservation equation of the radiationhydrodynamic model [1]. Particularly, we aim to simulate spatial-time evolution of a coupled system of plasma temperature and radiation field which is provoked by absorption of intense...

the compact finite difference schemes have been found to give simple ways of reaching the objectives of high accuracy and low computational cost. during the past two decades, the compact schemes have been used extensively for numerical simulation of various fluid dynamics problems. these methods have also been applied for numerical solution of some prototype geophysical fluid dynamics problems ...

We discuss the discretization using discontinuous Galerkin (DG) formulation of an elliptic Poisson problem. Two commonly used DG schemes are investigated: the original average flux proposed by Bassi and Rebay (J. Comput. Phys. 1997; 131:267) and the local discontinuous Galerkin (LDG) (SIAM J. Numer. Anal. 1998; 35:2440–2463) scheme. In this paper we expand on previous expositions (Discontinuous...

Three different high-order finite element methods are used to solve the advection problem—two implementations of a discontinuous Galerkin and a spectral element (high-order continuous Galerkin) method. The three methods are tested using a 2D Gaussian hill as a test function, and the relative L2 errors are compared. Using an explicit Runge–Kutta time stepping scheme, all three methods can be par...

In this paper we first briefly review the semi-analytical method [20] for solving the Derivative Riemann Problem for systems of hyperbolic conservation laws with source terms. Next, we generalize it to hyperbolic systems for which the Riemann problem solution is not available. As an application example we implement the new derivative Riemann solver in the high-order finite-volume ADER advection...

Abstract In [22], two of the authors constructed uniformly high order accurate finite volume and discontinuous Galerkin (DG) schemes satisfying a strict maximum principle for scalar conservation laws on rectangular meshes. The technique is generalized to positivity preserving (of density and pressure) high order DG or finite volume schemes for compressible Euler equations in [23]. The extension...

This paper reviews the main features of a high-order nondissipative discontinuous Galerkin (DG) method recently investigated in [1]-[3] for solving Maxwell’s equations on non-conforming simplex meshes. The proposed method combines a centered approximation for the numerical fluxes at inter element boundaries, with either a secondorder or a fourth-order leap-frog time integration scheme. Moreover...