Submitted for the DFD08 Meeting of The American Physical Society A low-numerical dissipation immersed interface method for the compressible Navier-Stokes equations CARLOS PANTANO, KOSTAS KARAGIOZIS, RAMJI KAMAKOTI, University of Illinois at Urbana-Champaign — Immersed interface methods are an alternative methodology to unstructured methods for solving fluid dynamical problems around complex geo...

Kinetic schemes for compressible flow of gases are constructed by exploiting the connection between Boltzmann equation and the Navier-Stokes equations. This connection allows us to construct a flux splitting for the NavierStokes equations based on the direction of molecular motion from which a numerical flux can be obtained. The naive use of such a numerical flux function in a discontinuous Gal...

We prove weak-strong uniqueness results for the isentropic compressible Navier-Stokes system on the torus. In other words, we give conditions on a strong solution so that it is unique in a class of weak solutions. Known weak-strong uniqueness results are improved. Classical uniqueness results for this equation follow naturally.

Abstract: We prove the existence of global weak solutions to the Navier-Stokes equations for compressible isentropic fluids for any γ > 1 when the Cauchy data are helically symmetric, where the constant γ is the specific heat ratio. Moreover, a new integrability estimate of the density in any neighborhood of the symmetry axis (the singularity axis) is obtained.

A general approach to the construction of discrete equilibrium distributions is presented. Such distribution functions can be used to set up Kinetic Schemes as well as Lattice Boltzmann methods. The general principles are also applied to the construction of Chapman Enskog distributions which are used in Kinetic Schemes for compressible Navier Stokes equations.

We consider a multidimensional model for the combustion of compressible reacting fluids. The flow is governed by the Navier-Stokes in Eulerian coordinates and the chemical reaction is irreversible and is governed by the Arrhenius kinetics. The existence of globally defined weak solutions is established by using weak convergence methods, compactness and interpolation arguments in the spirit of F...

This paper is concerned with the construction of global smooth solutions away from vacuum to the Cauchy problem of the one-dimensional compressible Navier-Stokes-Poisson system with large data and density dependent viscosity coefficient and density and temperature dependent heat conductivity coefficient. The proof is based on some detailed analysis on the bounds on the density and temperature f...

Grid adaptation is a very useful method for applications with unstructured meshes but requires dynamic load-balancing for efficient parallel computation. In this study, a parallel 3D compressible Navier-Stokes code with adaptive hybrid meshes (epHYBRID) and parallel adaptation procedure (pADAPT) have been developed on GeoFEM parallel platform. The DRAMA library has been integrated into the pADA...

We prove the global existence of weak solutions for the 2-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient (λ = λ(ρ)). Initial data and solutions are small in energy-norm with nonnegative densities having arbitrarily large sup-norm. Then, we show that if there is a vacuum domain at the initial time, then the vacuum domain will retain for all time, and vanish...

We study the incompressible limit of solutions to the compressible barotropic Navier-Stokes system in the exterior of a bounded domain undergoing a simple translation. The problem is reformulated using a change of coordinates to fixed exterior domain. Using the spectral analysis of the wave propagator, the dispersion of acoustic waves is proved by the means of the RAGE theorem. The solution to ...