Numerical flux formulas for the convection terms in the Euler or Navier-Stokes equations are analyzed with regard to their accuracy in representing steady nonlinear and linear waves (shocks and entropykhear waves, respectively). Numerical results are obtained for a one-dimensional conical Navier-Stokes flow including both a shock and a boundary layer. Analysis and experiments indicate that for ...

In the context of low Mach number flows, successful methods are Asymptotic Preserving and IMEX schemes. Both schemes for hyperbolic equations rely on a splitting of the convective flux into stiff and nonstiff parts. This choice is not arbitrary and has an influence on both the stability and the accuracy of the resulting methods. In this work, we consider a first-order IMEX scheme based on diffe...

two-dimensional euler equations have been solved on an unstructured grid. an upwind finite volume scheme, based on roes flux difference splitting method, is used to discretize the equations. using advancing front method, an initial delaunay triangulation has been made. the adaptation procedure involves mesh enrichment coarsening in regions of flow with high low gradients of flow properties, acc...

Various gaps in the surface of the supersonic aircraft have a significant effect on airflows. In order to predict the effects of attack angle, Mach number and width-to-depth ratio of gap on the local aerodynamic heating environment of supersonic flow, two-dimensional compressible Navier-Stokes equations are solved by the finite volume method, where convective flux of space term adopts the Roe f...

The theory of flux-corrected transport (FCT) developed by Boris and Book [.I. Co~~pur. P~JLV. II (1973) 38; 18 (1975) 248; 20 (1976) 3971 is placed in a simple, generalized format, and a new algorithm for implementing the critical flux limiting stage in multidimensions without resort to time splitting is presented. The new flux limiting algorithm shows the use of FCT techniques in multidimensio...

In this work, we propose a new way of splitting the flux function of the isentropic compressible Euler equations at low Mach number into stiff and non-stiff parts. Following the IMEX methodology, the latter ones are treated explicitly, while the first ones are treated implicitly. The splitting is based on the incompressible limit solution, which we call reference solution (RS). An analysis conc...

Two-dimensional Euler equations have been solved on an unstructured grid. An upwind finite volume scheme, based on Roes flux difference splitting method, is used to discretize the equations. Using advancing front method, an initial Delaunay triangulation has been made. The adaptation procedure involves mesh enrichment coarsening in regions of flow with high low gradients of flow properties, acc...

The Euler equations subject to uncertainty in the initial and boundary conditions are investigated via the stochastic Galerkin approach. We present a new fully intrusive method based on a variable transformation of the continuous equations. Roe variables are employed to get quadratic dependence in the flux function and a well-defined Roe average matrix that can be determined without matrix inve...

The gas-kinetic theory based flux splitting method has been successfully proposed for solving oneand two-dimensional ideal magnetohydrodynamics by Xu et al. [J. Comput. Phys., 1999; 2000], respectively. This paper extends the kinetic method to solve three-dimensional ideal magnetohydrodynamics equations, where an adaptive parameter η is used to control the numerical dissipation in the flux spli...

An approach to integrate transport equations with fluxes being complex non-linear functions of physical parameters and their gradients, as it is predicted by theoretical models for micro-instabilities in plasma, is proposed. This approach operates without any splitting of the flux on diffusive and convective components often involved in transport calculations. As an example, computations of the...