scholarly journals High-order unstructured Lagrangian one-step WENO finite volume schemes for non-conservative hyperbolic systems: Applications to compressible multi-phase flows

2013 ◽  
Vol 86 ◽  
pp. 405-432 ◽  
Author(s):  
Michael Dumbser ◽  
Walter Boscheri
Keyword(s):  
Finite Volume ◽  
Hyperbolic Systems ◽  
High Order ◽  
Finite Volume Schemes ◽  
One Step ◽  
Multi Phase

scholarly journals Arbitrary-Lagrangian-Eulerian One-Step WENO Finite Volume Schemes on Unstructured Triangular Meshes

2013 ◽  
Vol 14 (5) ◽  
pp. 1174-1206 ◽  
Author(s):  
Walter Boscheri ◽  
Michael Dumbser
Keyword(s):  
Finite Volume ◽  
Space Time ◽  
High Order ◽  
Finite Volume Scheme ◽  
Two Dimensional ◽  
Triangular Meshes ◽  
Finite Volume Schemes ◽  
Local Space ◽  
One Step ◽  
Time Basis

AbstractIn this article we present a new class of high order accurate Arbitrary-Eulerian-Lagrangian (ALE) one-step WENO finite volume schemes for solving nonlinear hyperbolic systems of conservation laws on moving two dimensional unstructured triangular meshes. A WENO reconstruction algorithm is used to achieve high order accuracy in space and a high order one-step time discretization is achieved by using the local space-time Galerkin predictor proposed in. For that purpose, a new element-local weak formulation of the governing PDE is adopted on moving space-time elements. The space-time basis and test functions are obtained considering Lagrange interpolation polynomials passing through a predefined set of nodes. Moreover, a polynomial mapping defined by the same local space-time basis functions as the weak solution of the PDE is used to map the moving physical space-time element onto a space-time reference element. To maintain algorithmic simplicity, the final ALE one-step finite volume scheme uses moving triangular meshes withstraightedges. This is possible in the ALE framework, which allows a local mesh velocity that is different from the local fluid velocity. We present numerical convergence rates for the schemes presented in this paper up to sixth order of accuracy in space and time and show some classical numerical test problems for the two-dimensional Euler equations of compressible gas dynamics.

A REVIEW ON HIGH ORDER WELL-BALANCED PATH-CONSERVATIVE FINITE VOLUME SCHEMES FOR GEOPHYSICAL FLOWS

2019 ◽  
Author(s):  
MANUEL J. CASTRO ◽  
MARC DE LA ASUNCIÓN ◽  
ENRIQUE D. FERNÁNDEZ NIETO ◽  
JOSÉ M. GALLARDO ◽  
JOSÉ M. GONZÁLEZ VIDA ◽  
...  
Keyword(s):  
Finite Volume ◽  
High Order ◽  
Geophysical Flows ◽  
Finite Volume Schemes
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