To increase the numerical accuracy in solving engineering problems, either conventional methods on a fine grid or methods with a high order of accuracy on a coarse grid can be used. In the present research, the second approach is utilized and the arbitrary high order Discontinues Galerkin Arbitrary DERivative (DG-ADER) method is applied to analyze the transient isothermal flow of natural gas th...

In this paper, we develop a fully discrete entropy preserving ADER-Discontinuous Galerkin (ADER-DG) method. To obtain desired result, equip the space part of method with correction terms that balance production in space, inspired by work Abgrall. Whereas for time-discretization apply relaxation approach introduced Ketcheson allows to modify timestep preserve machine precision. Up our knowledge,...

This paper presents a numerical scheme of arbitrary order accuracy in both space and time, based on the high-order derivatives methodology, for transient acoustic simulations. The combines nodal discontinuous Galerkin method spatial discretization Taylor series integrator (TSI) time integration. main idea TSI is temporal expansion all unknown variables which are replaced by via Cauchy-Kovalewsk...

We present results of thorough benchmarking of an arbitrary high-order derivative discontinuous Galerkin (ADER-DG) method on unstructured meshes for advanced earthquake dynamic rupture problems. We verify the method by comparison to well-established numerical methods in a series of verification exercises, including dipping and branching fault geometries, heterogeneous initial conditions, bimate...

In this paper we apply the ADER one step time discretization to the Discontinuous Galerkin framework for hyperbolic conservation laws. In the case of linear hyperbolic systems we obtain a quadrature-free explicit single-step scheme of arbitrary order of accuracy in space and time on Cartesian and triangular meshes. The ADERDG scheme does not need more memory than a first order explicit Euler ti...

The purpose of this work is to propose a novel a posteriori finite volume subcell limiter technique for the Discontinuous Galerkin finite element method for nonlinear systems of hyperbolic conservation laws in multiple space dimensions that works well for arbitrary high order of accuracy in space and time and that does not destroy the natural subcell resolution properties of the DG method. High...

s of presentations E. F. Toro Mathematical modelling, numerical simulation and high-order ADER schemes In this lecture I review some basic concepts regarding the mathematical modelling of processes in physics and other disciplines and their numerical simulation. There follows a discussion on the issue of high-order of accuracy of numerical methods, its misconceptions and eventual justification....

Abstract In this work, we present a novel numerical discretization of variable pressure multilayer shallow water model. The model can be written as hyperbolic PDE system and allows the simulation density driven gravity currents in framework. proposed consists an unlimited arbitrary high order accurate (ADER) Discontinuous Galerkin (DG) method, which is then limited with MOOD paradigm using post...

We study in this paper three variants of the high-order Discontinuous Galerkin (DG) method with Runge-Kutta (RK) time integration for induction equation, analysing their ability to preserve divergence-free constraint magnetic field. To quantify divergence errors, we use a norm based on both surface term, measuring global and volume local errors. This leads us design new, arbitrary numerical sch...

We present a new version of conservative ADER-WENO finite volume schemes, in which both the high order spatial reconstruction as well as the time evolution of the reconstruction polynomials in the local space-time predictor stage are performed in primitive variables, rather than in conserved ones. To obtain a conservative method, the underlying finite volume scheme is still written in terms of ...