This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor fiowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid ...

The aim of this work is to derive a well-balanced numerical scheme to approximate the solutions of the Euler equations with a gravitational potential. This system admits an infinity of steady state solutions which are not all known in an explicit way. Among all these solutions, the hydrostatic atmosphere has a special physical interest. We develop an approximate Riemann solver using the formali...

This paper deals with intrusive Galerkin projection methods with Roe-type solver for uncertain hyperbolic systems using a finite volume discretization in physical space and a piecewise continuous representation at the stochastic level. The aim of this paper is to design a cost-effective adaptation of the deterministic Dubois and Mehlman corrector to avoid entropy-violating shocks in the presenc...

There are two stages in the 1st-order Godunov-type schemes to update ow variables, the gas evolution stage for the numerical uxes across cell interface and the projection stage for the reconstruction of constant state inside each cell. Ideally, the evolution stage should be based on the exact Euler solutions, the so-called Riemann solver. In this paper, we will show that some anomalous phenomen...

When a droplet impacts a solid surface at high speed, the contact periphery expands very quickly and liquid compressibility plays an important role in the initial dynamics and the formation of lateral jets. The high speed impact results in high pressures that can account for the surface erosion. In this study, we numerically investigated a high speed droplet impacts on a solid wall. The multico...

Numerical solution of the stationary navier-stokes equations by means of a multiple grid method and newton iteration. Distributive iterationen f ur indeenite Systeme als Gll atter in Mehrgitter-verfahren am Beispiel der Stokes-und Navier-Stokes-Gleichungen mit Schwerpunkt auf unvollstt andingen Zerlegungen. PhD thesis, Christan-Albrechts Universitt at, Kiel, 1986. 145. G. Wittum. Linear iterati...

Abstract We present a three-dimensional (3D) numerical solver of the linearized compressible Euler equations (Global Acoustic Linearized Euler), used to model acoustic oscillations throughout solar interior. The governing are solved in conservation form on fully global spherical mesh (0 ? ? 2 ? , 0 ? r R ? ) over background state generated by standard S. implement an efficient pseudospectral co...

The main goal of this paper is to analyze the exergy losses during the shock and rarefaction wave of hydrogen-air mixture. First, detonation parameters pressure, temperature, density, and species mass fraction are calculated for three cases where the hydrogen mass fraction in air is 1.5%, 2.5%, and 5%. Then, exergy efficiency is used as objective criteria of performance evaluation. A two-dimens...

Residual distributions (RD) schemes are a class of of high-resolution finite volume methods for unstructured grids. A key feature of these schemes is that they make use of genuinely multidimensional (approximate) Riemann solvers as opposed to the piecemeal 1D Riemann solvers usually employed by finite volume methods. In 1D, LeVeque and Pelanti [J. Comp. Phys. 172, 572 (2001)] showed that many o...

An implicit method for the solution of the 3D supersonic Euler equations is presented. The numerical technique adopted is a nite volume method based on an unfactored implicit upwind scheme. A great relevance is given to the deenition of the implicit operator and to the solution of the linear systems. A preconditioned iterative solver has been used showing better performance than unpreconditione...