A 3D finite element ALE method using an approximate Riemann solution. (9th August 2016)

• Record Type: Journal Article
• Authors: Chiravalle, V. P.; Morgan, N. R.
• Is Part Of: International journal for numerical methods in fluids. Volume 83:Number 8(2017)
• Page Start: 642
• Page End: 663
• Publication Date: 2016-08-09
• Subjects: ALE -- finite element method -- approximate Riemann solution; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4284
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann‐like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann‐like problem. Two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well‐known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problem results are presented. Copyright © 2016 John Wiley & Sons, Ltd. Abstract : A finite element arbitrary Lagrangian–Eulerian method that solves a multidirectional Riemann‐like problem incorporating two limiting coefficients: the first is based on the minmod limiter and the second is a function of the discrete Mach number is presented. Our approach produces substantially less internal energy errors than the minmod limiter alone for a steel shell implosion as shown in Figure 1. For strong shock problems, the new limiter is more accurate and converges at a higher rate than the quadratic artificial viscosity.