Simplified second-order Godunov-type methods
SIAM Journal on Scientific and Statistical Computing
Journal of Computational Physics
A multiphase Godunov method for compressbile multifluid and multiphase flows
Journal of Computational Physics
A high-order Eulerian Godunov method for elastic-plastic flow in solids
Journal of Computational Physics
Computations of compressible multifluids
Journal of Computational Physics
A free-Lagrange augmented Godunov method for the simulation of elastic-plastic solids
Journal of Computational Physics
Coupling an Eulerian fluid calculation to a Lagrangian solid calculation with the ghost fluid method
Journal of Computational Physics
Mathematical and numerical modeling of two-phase compressible flows with micro-inertia
Journal of Computational Physics
A conservative three-dimensional Eulerian method for coupled solid-fluid shock capturing
Journal of Computational Physics
Discrete equations for physical and numerical compressible multiphase mixtures
Journal of Computational Physics
Modelling detonation waves in heterogeneous energetic materials
Journal of Computational Physics
A five equation reduced model for compressible two phase flow problems
Journal of Computational Physics
Modelling evaporation fronts with reactive Riemann solvers
Journal of Computational Physics
Journal of Computational Physics
Modelling wave dynamics of compressible elastic materials
Journal of Computational Physics
A conservative level-set based method for compressible solid/fluid problems on fixed grids
Journal of Computational Physics
Eulerian adaptive finite-difference method for high-velocity impact and penetration problems
Journal of Computational Physics
An Eulerian algorithm for coupled simulations of elastoplastic-solids and condensed-phase explosives
Journal of Computational Physics
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Diffuse interface methods have been recently proposed and successfully used for accurate compressible multi-fluid computations Abgrall [1]; Kapila et al. [20]; Saurel et al. [30]. These methods deal with extended systems of hyperbolic equations involving a non-conservative volume fraction equation and relaxation terms. Following the same theoretical frame, we derive here an Eulerian diffuse interface model for elastic solid-compressible fluid interactions in situations involving extreme deformations. Elastic effects are included following the Eulerian conservative formulation proposed in Godunov [16], Miller and Colella [23], Godunov and Romenskii [17], Plohr and Plohr [27] and Gavrilyuk et al. [14]. We apply first the Hamilton principle of stationary action to derive the conservative part of the model. The relaxation terms are then added which are compatible with the entropy inequality. In the limit of vanishing volume fractions the Euler equations of compressible fluids and a conservative hyperelastic model are recovered. It is solved by a unique hyperbolic solver valid at each mesh point (pure fluid, pure solid and mixture cell). Capabilities of the model and methods are illustrated on various tests of impacts of solids moving in an ambient compressible fluid.