Jonas Zeifang

• PostDoc Position at Hasselt University

We present a dynamic load balancing scheme for compressible two-phase flows simulations using a high-order level-set ghost-fluid method. The load imbalance arises from introducing an element masking that applies the costly interface-tracking algorithm only to the grid cells near the phase interface. The load balancing scheme is based on a static do...

In this paper, we use an implicit two-derivative deferred correction time discretization approach and combine it with a spatial discretization of the discontinuous Galerkin spectral element method to solve (non-)linear PDEs. The resulting numerical method is high order accurate in space and time. As the novel scheme handles two time derivatives, th...

Very recently, a novel class of parallelizable high-order time discretization schemes has been introduced in Schütz et al. (J Sci Comput 90(54):1–33, 2022). In this current work, we analyze the stability properties of those schemes and introduce a small but effective modification which only necessitates minor modifications of existing implementatio...

Based on the recent development of Jacobian-free Lax–Wendroff (LW) approaches for solving hyperbolic conservation laws (Zorio et al. in J Sci Comput 71:246–273, 2017, Carrillo and Parés in J Sci Comput 80:1832–1866, 2019), a novel collection of explicit Jacobian-free multistage multiderivative solvers for hyperbolic conservation laws is presented i...

In this work, we present a novel class of high-order time integrators for the numerical solution of ordinary differential equations. These integrators are of the two-derivative type, i.e., they take into account not only the first, but also the second temporal derivative of the unknown solution. While being motivated by two-derivative Runge–Kutta s...

In this paper, we use an implicit two-derivative deferred correction time discretization approach and combine it with a spatial discretization of the discontinuous Galerkin spectral element method to solve (non-)linear PDEs. The resulting numerical method is high order accurate in space and time. As the novel scheme handles two time derivatives, th...

Considering droplet phenomena at low Mach numbers, large differences in the magnitude of the occurring characteristic waves are presented. As acoustic phenomena often play a minor role in such applications, classical explicit schemes which resolve these waves suffer from a very restrictive timestep restriction. In this work, a novel scheme based on...

Based on the recent development of Jacobian-free Lax-Wendroff (LW) approaches for solving hyperbolic conservation laws [Zorio, Baeza and Mulet, Journal of Scientific Computing 71:246-273, 2017], [Carrillo and Par\'es, Journal of Scientific Computing 80:1832-1866, 2019], a novel collection of explicit Jacobian-free multistage multiderivative solvers...

In this work, we present a novel higher-order smooth artificial viscosity method for the discontinuous Galerkin spectral element method and related high order methods. A neural network is used to detect the need for stabilization. Inspired by techniques from image edge detection, the neural network locates discontinuities inside mesh elements on a...

In this work, we present a novel higher-order smooth artificial viscosity method for the discontinuous Galerkin spectral element method and related high order methods. A neural network is used to detect the need for stabilization. Inspired by techniques from image edge detection, the neural network locates discontinuities inside mesh elements on a...

In this work, we present a novel class of parallelizable high-order time integration schemes for the approximate solution of additive ODEs. The methods achieve high order through a combination of a suitable quadrature formula involving multiple derivatives of the ODE's right-hand side and a predictor-corrector ansatz. The latter approach is designe...

Considering droplet phenomena at low Mach numbers, large differences in the magnitude of the occurring characteristic waves are present. As acoustic phenomena often play a minor role in such applications, classical explicit schemes which resolve these waves suffer from a very restrictive timestep restriction. In this work, a novel scheme based on a...

The stable and accurate approximation of discontinuities such as shocks on a finitecomputational mesh is a challenging task. Detection of shocks or strong discontinuitiesin the flow solution is typically achieved through a priori troubled cell indicators, whichguide the subsequent action of an appropriate shock capturing mechanism. Arriving ata sta...

For the accurate and efficient discretization of the low-Mach isentropic Euler equations, which can be used for the description of droplet dynamics, several IMEX splitting schemes have been introduced in literature. In this work, we cast multiple splittings into a common framework, which makes it possible to compare them numerically. Temporal discr...

This paper describes improvements of a level-set ghost-fluid algorithm in the scope of sharp interface multi-phase flow simulations. The method is used to simulate drop-drop and shock-drop interactions. Both, the level-set and the bulk phases are discretized by a high order discontinuous Galerkin spectral element method. The multi-phase interface a...

In this paper we propose a novel regularization strategy for the local discontinuous Galerkin method to solve the Hamilton-Jacobi equation in the context of level-set reinitialization. The novel regularization idea works in analogy to shock-capturing schemes for discontinuous Galerkin methods, which are based on finite volume sub-cells. In this spi...

The stable and accurate approximation of discontinuities such as shocks on a finite computational mesh is a challenging task. Detection of shocks or strong discontinuities in the flow solution is typically achieved through a priori troubled cell indicators, which guide the subsequent action of an appropriate shock capturing mechanism. Arriving at a...

This paper summarizes our progress in the application and feature development of a high-order discontinuous Galerkin (DG) method for scale resolving fluid dynamics simulations on the Cray XC40 Hazel Hen cluster at HLRS. We present the extension to Chimera grid techniques which allow efficient computations on flexible meshes, and discuss data-based...

In this paper, we introduce an extension of a splitting method for singularly perturbed equations, the so-called RS-IMEX splitting [Kaiser et al., Journal of Scientific Computing, 70(3), 1390-1407], to deal with the fully compressible Euler equations. The straightforward application of the splitting yields sub-equations that are, due to the occurre...

In this work, we consider the efficient approximation of low-Mach flows by a high-order scheme. This scheme is a coupling of a discontinuous Galerkin (DG) discretization in space and an implicit/explicit (IMEX) dis-cretization in time. The splitting into linear implicit and nonlinear explicit parts relies heavily on the incompressible solution. The...