81 citations · 149 across the 8 of their papers we have counts for
13 papers
Fully Discrete Active Flux Methods for the Euler Equations: Exploring Different Reconstructions and New Multi-Dimensional Evolution Operators
Christiane Helzel, Mária Lukáčová-Medvid'ová, Amelie Porfetye +1
We present new fully discrete Cartesian grid Active Flux methods for the two-dimensional Euler equations of gas dynamics. A key component of these methods is the evolution operator…
Perspectives on Sustainable Computational Science and Engineering
Julia Kowalski, Ann S. Almgren, Achim Basermann +43
Computational Science and Engineering (CSE) combines expertise at the intersection of engineering, applied mathematics, and computer science to form powerful methods for model-base…
A Comparison of Active Flux Methods for the Vlasov-Poisson System
Lukas Hensel, Yanick Kiechle, Rainer Grauer +3
Active Flux is a third-order accurate, fairly novel finite volume method for hyperbolic conservation laws that is becoming increasingly popular. It evolves additional nodal degrees…
A fully discrete Active Flux method for the Euler equations comparing different truly multi-dimensional evolution operators
Christiane Helzel, Amelie Porfetye
This article builds upon our recently published fully discrete Cartesian grid Active Flux method for the Euler equations by introducing a new evolution operator for the linearized…
New Fully Discrete Active Flux Methods with Truly Multi-Dimensional Evolution Operators and WENO Reconstruction
Amelie Porfetye, Zhuyan Tang, Shaoshuai Chu +2
We propose new fully discrete third-order accurate Active Flux and WENO methods based on truly multidimensional evolution operators for the two-dimensional acoustic equations. Buil…
A Fully Discrete Truly Multidimensional Active Flux Method For The Two-Dimensional Euler Equations
Erik Chudzik, Christiane Helzel, Amelie Porfetye
The Active Flux method is a finite volume method for hyperbolic conservation laws that uses both cell averages and point values as degrees of freedom. Several versions of such meth…
Numerical Discretisation of Hyperbolic Systems of Moment Equations Describing Sedimentation in Suspensions of Rod-Like Particles
Sina Dahm, Jan Giesselmann, Christiane Helzel
We present a numerical discretisation of the coupled moment systems, previously introduced in Dahm and Helzel, which approximate the kinetic multi-scale model by Helzel and Tzavara…
The Cartesian Grid Active Flux Method with Adaptive Mesh Refinement
Donna Calhoun, Erik Chudzik, Christiane Helzel
We present the first implementation of the Active Flux method on adaptively refined Cartesian grids. The Active Flux method is a third order accurate finite volume method for hyper…
Improved Accuracy of High-Order WENO Finite Volume Methods on Cartesian Grids
Pawel Buchmüller, Christiane Helzel
We propose a simple modification of standard WENO finite volume methods for Cartesian grids, which retains the full spatial order of accuracy of the one-dimensional discretization…
A comparison of macroscopic models describing the collective response of sedimenting rod-like particles in shear flows
Christiane Helzel, Athanasios E. Tzavaras
We consider a kinetic model, which describes the sedimentation of rod-like particles in dilute suspensions under the influence of gravity. This model has recently been derived by H…
A kinetic model for the sedimentation of rod-like particles
Christiane Helzel, Athanasios E. Tzavaras
We consider a coupled system consisting of a kinetic equation coupled to a macroscopic Stokes (or Navier-Stokes) equation and describing the motion of a suspension of rigid rods in…
A high-order unstaggered constrained transport method for the 3D ideal magnetohydrodynamic equations based on the method of lines
Christiane Helzel, James A. Rossmanith, Bertram Taetz
Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must confront the challenge of controlling errors in the discrete diver…
An Unstaggered Constrained Transport Method for the 3D Ideal Magnetohydrodynamic Equations
Christiane Helzel, James A. Rossmanith, Bertram Taetz
Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must either confront the challenge of controlling errors in the discret…