A nodal Godunov method for Lagrangian shock hydrodynamics on unstructured tetrahedral grids

Abstract

SUMMARYWe present a nodal Godunov method for Lagrangian shock hydrodynamics. The method is designed to operate on three‐dimensional unstructured grids composed of tetrahedral cells. A node‐centered finite element formulation avoids mesh stiffness, and an approximate Riemann solver in the fluid reference frame ensures a stable, upwind formulation. This choice leads to a non‐zero mass flux between control volumes, even though the mesh moves at the fluid velocity, but eliminates volume errors that arise due to the difference between the fluid velocity and the contact wave speed. A monotone piecewise linear reconstruction of primitive variables is used to compute interface unknowns and recover second‐order accuracy. The scheme has been tested on a variety of standard test problems and exhibits first‐order accuracy on shock problems and second‐order accuracy on smooth flows using meshes of up to O(106) tetrahedra. Copyright © 2014 John Wiley & Sons, Ltd.

Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part I: The one-dimensional case

“…Indeed, in this particular frame, the momentum and total energy conservation equations are solved on the dual grid around the nodes, generally by means of an edge-based finite element scheme or an edge-based upwind finite volume method. The PCH approach has been successful applied these past decades to problematics concerned with the simulation of incompressible flows, compressible Lagrangian flows, or Lagrangian solid dynamics, refer for instance to [28,29,24,42,48,76,79,78,86,87,67,68,2,3]. Two of the main advantages of these schemes are that there are very well adapted to triangular or tetrahedral grids, as well as they reduce in most cases problems related to mesh stiffness.…”

Study on a matter flux method for staggered essentially Lagrangian hydrodynamics on triangular grids

“…A simple approach is letting the momentum variance in an element distribute evenly on its three nodes. Taking element K Nb for example, we can have its momentum variation (ΔMu 12 ) distributed evenly on its three nodes of B, C, and D, that is, each node receives a momentum of (Δmu 12 ), with Δm defined in (37). Similarly, considering the element K, each of its three nodes A, B, and D receives a momentum of (−Δmu 12 ) from it.…”

“…The introduction of fluxes that allow matter migration among control volumes in Lagrangian simulations has been tried by many authors. 1 In the PCH studied by Morgan et al, 36,37 the authors pointed out that in the ordinary Godunov scheme the volume rate is not precisely captured by the volume evolution equation, which leads to oscillations near discontinuities. In order to compensate for this volume error, the authors introduced the Rusanov flux which allows mass migration among nodal control volumes.…”

Performance analysis of a 3D unstructured mesh hydrodynamics code on multi‐core and many‐core architectures

“…The methods and algorithms under consideration have been described extensively elsewhere [7][8][9][10], and because the emphasis of this work is performance analysis of the existing algorithms rather …”

“…The methods and algorithms under consideration have been described extensively elsewhere [7][8][9][10], and because the emphasis of this work is performance analysis of the existing algorithms rather than the description of new algorithms, only a high-level summary is provided here. The host code solves the arbitrary Lagrangian-Eulerian (ALE) form of the compressible hydrodynamic equations, written here in the flux conservative form…”