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In this paper, we present a novel second-order accurate Arbitrary-Lagrangian-Eulerian (ALE) finite volume scheme on moving nonconforming polygonal grids, in order to avoid the typical mesh distortion caused by shear flows in Lagrangian-type…

Numerical Analysis · Mathematics 2017-10-31 Elena Gaburro , Michael Dumbser , Manuel J. Castro

In this paper we present a conservative cell-centered Lagrangian finite volume scheme for the solution of the hyper-elasticity equations on unstructured multidimensional grids. The starting point of the new method is the Eucclhyd scheme,…

Numerical Analysis · Mathematics 2021-04-07 Walter Boscheri , Raphaël Loubère , Pierre-Henri Maire

This study proposes an extension of the high-order compact gas-kinetic scheme (CGKS) to compressible flow simulation in an arbitrary Lagrangian-Eulerian (ALE) formulation in unstructured mesh. The ALE method is achieved by subdividing…

Computational Physics · Physics 2024-01-05 Yue Zhang , Kun Xu

In this work we present a novel second order accurate well balanced Arbitrary-Lagrangian-Eulerian (ALE) finite volume scheme on moving nonconforming meshes for the Euler equations of compressible gasdynamics with gravity in cylindrical…

Numerical Analysis · Mathematics 2018-03-16 Elena Gaburro , Manuel J. Castro , Michael Dumbser

There is a great need in several areas of astrophysics and space-physics to carry out high order of accuracy, divergence-free MHD simulations on spherical meshes. This requires us to pay careful attention to the interplay between mesh…

A high-order finite difference numerical scheme is developed for the ideal magnetohydrodynamic equations based on an alternative flux formulation of the weighted essentially non-oscillatory (WENO) scheme. It computes a high-order numerical…

Numerical Analysis · Mathematics 2018-07-10 Andrew J. Christlieb , Xiao Feng , Yan Jiang , Qi Tang

For the arbitrary-Lagrangian-Eulerian (ALE) calculations, the geometric information needs to be calculated at each time step due to the movement of mesh. To achieve the high-order spatial accuracy, a large number of matrix inversions are…

Computational Physics · Physics 2025-08-18 Yibo Wang , Xing Ji , Liang Pan

This paper develops the structure-preserving finite volume weighted essentially non-oscillatory (WENO) hybrid schemes for the shallow water equations under the arbitrary Lagrangian-Eulerian (ALE) framework, dubbed as ALE-WENO schemes. The…

Numerical Analysis · Mathematics 2023-02-24 Jiahui Zhang , Yinhua Xia , Yan Xu

We present a one-dimensional high-order moving-mesh finite element method for moving boundary problems where the boundary velocity depends implicitly on the solution in the interior of the domain. The method employs a conservative arbitrary…

Numerical Analysis · Mathematics 2025-09-05 Matthew E Hubbard , Thomas J Radley

In this report, we propose a collection of methods to make such an approach possible for Euler equations in one and two dimensions. We propose an explicit single-step ALE DG scheme for hyperbolic conservation laws. The scheme considerably…

Numerical Analysis · Mathematics 2023-03-09 Jayesh Badwaik

In this paper we present a novel arbitrary high order accurate discontinuous Galerkin (DG) finite element method on space-time adaptive Cartesian meshes (AMR) for hyperbolic conservation laws in multiple space dimensions, using a high order…

Numerical Analysis · Mathematics 2015-09-03 Olindo Zanotti , Francesco Fambri , Michael Dumbser , Arturo Hidalgo

In this paper, a simple and efficient third-order weighted essentially non-oscillatory (WENO) reconstruction is developed for three-dimensional flows, in which the idea of two-dimensional WENO-AO scheme on unstructured meshes…

Numerical Analysis · Mathematics 2019-09-05 Liang Pan , Kun Xu

This paper presents robust discontinuous Galerkin methods for the incompressible Navier-Stokes equations on moving meshes. High-order accurate arbitrary Lagrangian-Eulerian formulations are proposed in a unified framework for both…

Computational Physics · Physics 2021-03-17 Niklas Fehn , Johannes Heinz , Wolfgang A. Wall , Martin Kronbichler

We develop new adaptive alternative weighted essentially non-oscillatory (A-WENO) schemes for hyperbolic systems of conservation laws. The new schemes employ the recently proposed local characteristic decomposition based central-upwind…

Numerical Analysis · Mathematics 2022-11-15 Alina Chertock , Shaoshuai Chu , Alexander Kurganov

This study presents the development of a compact gas-kinetic scheme using an arbitrary Lagrangian-Eulerian (ALE) formulation for structured meshes. Unlike the Eulerian formulation, the ALE approach effectively tracks flow discontinuities,…

Computational Physics · Physics 2026-02-11 Yue Zhang , Xing Ji , Yibing Chen , Fengxiang Zhao , Kun Xu

In this paper we propose a new high order accurate space-time DG finite element scheme for the solution of the linear elastic wave equations in first order velocity-stress formulation in two and three-space dimensions on staggered…

Numerical Analysis · Mathematics 2018-05-09 Maurizio Tavelli , Michael Dumbser

In this paper, a third-order weighted essentially non-oscillatory (WENO) scheme is developed for hyperbolic conservation laws on unstructured quadrilateral and triangular meshes. As a starting point, a general stencil is selected for the…

Numerical Analysis · Mathematics 2018-11-14 Fengxiang Zhao , Liang Pan , Shuanghu Wang

We propose a class of weighted compact central (WCC) schemes for solving hyperbolic conservation laws. The linear version can be considered as a high-order extension of the central Lax-Friedrichs (LxF) scheme and the central conservation…

Numerical Analysis · Mathematics 2022-07-20 Hua Shen , Matteo Parsani

Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes have been constructed for conservation laws. For multidimensional problems, they offer high order accuracy at a fraction of the cost of a finite volume WENO…

Numerical Analysis · Mathematics 2023-04-19 Dinshaw S. Balsara , Deepak Bhoriya , Chi-Wang Shu , Harish Kumar

In this paper, we propose a new unified first order hyperbolic model of Newtonian continuum mechanics coupled with electro-dynamics. The model is able to describe the behavior of moving elasto-plastic dielectric solids as well as viscous…

Fluid Dynamics · Physics 2017-09-13 Michael Dumbser , Ilya Peshkov , Evgeniy Romenski , Olindo Zanotti