An unsplit, higher order Godunov method for scalar conservation laws in multiple dimensions
Journal of Computational Physics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Multidimensional upwind methods for hyperbolic conservation laws
Journal of Computational Physics
A 3D adaptive mesh refinement algorithm for multimaterial gas dynamics
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
A conservative formulation for plasticity
Advances in Applied Mathematics
Three-dimensional adaptive mesh refinement for hyperbolic conservation laws
SIAM Journal on Scientific Computing
An unsplit 3D upwind method for hyperbolic conservation laws
Journal of Computational Physics
A front tracking method for compressible flames in one dimension
SIAM Journal on Scientific Computing
An adaptive Cartesian grid method for unsteady compressible flow in irregular regions
Journal of Computational Physics
A high-order Godunov method for multiple condensed phases
Journal of Computational Physics
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
A high-order Eulerian Godunov method for elastic-plastic flow in solids
Journal of Computational Physics
Journal of Computational Physics
Second-order accurate volume-of-fluid algorithms for tracking material interfaces
Journal of Computational Physics
An unsplit Godunov method for ideal MHD via constrained transport
Journal of Computational Physics
A Cartesian grid embedded boundary method for hyperbolic conservation laws
Journal of Computational Physics
Journal of Computational Physics
A conservative interface method for compressible flows
Journal of Computational Physics
A sharp interface immersed boundary method for compressible viscous flows
Journal of Computational Physics
Journal of Computational Physics
Accurate monotonicity- and extrema-preserving methods through adaptive nonlinear hybridizations
Journal of Computational Physics
Multi-material interface reconstruction on generalized polyhedral meshes
Journal of Computational Physics
Block structured adaptive mesh and time refinement for hybrid, hyperbolic+N-body systems
Journal of Computational Physics
Modelling wave dynamics of compressible elastic materials
Journal of Computational Physics
An unsplit Godunov method for ideal MHD via constrained transport in three dimensions
Journal of Computational Physics
Short Note: Analytical and geometrical tools for 3D volume of fluid methods in general grids
Journal of Computational Physics
Short Note: A limiter for PPM that preserves accuracy at smooth extrema
Journal of Computational Physics
Solid-fluid diffuse interface model in cases of extreme deformations
Journal of Computational Physics
A lattice Boltzmann approach for free-surface-flow simulations on non-uniform block-structured grids
Computers & Mathematics with Applications
An Eulerian method for multi-component problems in non-linear elasticity with sliding interfaces
Journal of Computational Physics
An Eulerian hybrid WENO centered-difference solver for elastic-plastic solids
Journal of Computational Physics
Discretization of hyperelasticity on unstructured mesh with a cell-centered Lagrangian scheme
Journal of Computational Physics
A Second-Order Accurate Conservative Front-Tracking Method in One Dimension
SIAM Journal on Scientific Computing
Petascale block-structured AMR applications without distributed meta-data
Euro-Par'11 Proceedings of the 17th international conference on Parallel processing - Volume Part II
Parallel, grid-adaptive approaches for relativistic hydro and magnetohydrodynamics
Journal of Computational Physics
A Three-Dimensional, Unsplit Godunov Method for Scalar Conservation Laws
SIAM Journal on Scientific Computing
Deforming composite grids for solving fluid structure problems
Journal of Computational Physics
A conservative level-set based method for compressible solid/fluid problems on fixed grids
Journal of Computational Physics
A simple second order cartesian scheme for compressible Euler flows
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
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.58 |
A new method is presented for the explicit Eulerian finite difference computation of shock capturing problems involving multiple resolved material phases in three dimensions. We solve separately for each phase the equations of fluid dynamics or solid mechanics, using as interface boundary conditions artificially extended representations of the individual phases. For fluids we use a new 3D spatially unsplit implementation of the piecewise parabolic (PPM) method of Colella and Woodward. For solids we use the 3D spatially unsplit Eulerian solid mechanics method of Miller and Colella. Vacuum and perfectly incompressible obstacles may also be employed as phases.A separate problem is the time evolution of material interfaces, which are represented by planar segments constructed with a volume-of-fluid method. The volume fractions are advanced in time using a second-order 3D spatially unsplit advection routine with a velocity field determined by solution of interface-normal two-phase Riemann problems. From the Riemann problem solutions we also determine cross-interface momentum and energy fluxes.The volume fractions in mixed cells may be arbitrarily small, which would ordinarily make the Courant-Friedrichs-Lewy time step stability limit arbitrarily small as well. We overcome this limitation using the mass-redistribution formalism to conservatively redistribute generalized mass in the neighborhood of the split cells.We present an application of this method to an explosion contained in a metal can: a reactive fluid (approximating PBX 9404) is encased within an elastic-plastic solid (approximating copper) surrounded by vacuum. Our implementation is in parallel, and with adaptive mesh refinement.