In this paper, we design stable and accurate numerical schemes for conservation laws with stiff source terms. A prime example and the main motivation for our study is the reactive Euler equations of gas dynamics. Furthermore, we consider widely studied scalar model equations. We device one-step IMEX (implicit-explicit) schemes for these equations that treats the convection terms explicitly and ...

The Implicit Continuous-fluid Eulerian (ICE) method is a successful and widely used semi-implicit finitevolume method that applies to flows that range from supersonic to subsonic regimes. The classical ICE method has been expanded to problems in multiphase flow which span a wide area of science and engineering. The ICE method is utilized by the C-SAFE code Uintah written at the University of Ut...

Well balanced or asymptotic preserving schemes are receiving an increasing amount of interest. This paper gives a precise setting for studying both properties in the case of Euler system with friction. We derive a simple solver which, by construction, preserves discrete equilibria and reproduces at the discrete level the same asymptotic behavior as that of the solutions of the continuous system...

The thin-layer Navier-Stokes equations are solved for two complete missile configurations on an IBM 3090-200 vectro-facility supercomputer. The conservation form of the three-dimensional equations, written in generalized coordinates, are finite differenced and solved on a body-fitted curvilinear grid system developed in conjunction with the flowfield solver. The numerical procedure is based on ...

We present an extensible Julia-based solver for the Euler equations that uses a summationby-parts (SBP) discretization on unstructured triangular grids. While SBP operators have been used for tensor-product discretizations for some time, they have only recently been extended to simplices. Here we investigate the accuracy and stability properties of simplexbased SBP discretizations of the Euler ...

We describe a numerical method for modeling temperature-dependent fluid flow coupled to heat transfer in solids. This approach to conjugate-heat-transfer can be used to compute transient and steady-state solutions to a wide range of fluid-solid systems in complex twoand three-dimensional geometry. Fluids are modeled with the temperature dependent incompressible Navier-Stokes equations using the...

This paper presents an approach, which combines the conventional finite volume method (FVM) with the lattice Boltzmann Method (LBM), to simulate compressible flows. Similar to the Godunov scheme, in the present approach, LBM is used to evaluate the flux at the interface for local Riemann problem when solving Euler/Navier-Stokes (N-S) equations by FVM. Two kinds of popular compressible Lattice B...

We are interested in an Eulerian–Lagrangian model describing particulate flows. The model under study consists of the Euler system and a Vlasov-Fokker-Planck equation coupled through momentum and energy exchanges. This problem contains asymptotic regimes that make the coupling terms stiff, and lead to a limiting model of purely hydrodynamic type. We design a numerical scheme which is able to ca...

We propose a relaxation framework for general fluid models which can be understood as a natural extension of the Suliciu approach in the Euler setting. In particular, the relaxation system may be totally degenerate. Several stability properties are proved. The relaxation procedure is shown to be efficient in the numerical approximation of the entropy weak solutions of the original PDEs. The num...