Order Godunov Scheme Research Articles

Barriers and challenges in computational fluid dynamics

Preface. 1: Accuracy. Progress in Applied Numerical Analysis for Computational Fluid Dynamics M.B. Giles. Examples of Error Propagation from Discontinuities B. Engquist, B. Sjogreen. Accurate Finite Difference Algorithms J.V. Goodrich. Computational Considerations for the Simulation of Discontinuous Flows M. H. Carpenter, J.H. Casper. Space-Time Methods for Hyperbolic Conservation Laws R.B. Lowrie, et al. II: Boundary Conditions and Stiffness Issues. Anisotropic Mesh Adaptation: A Step Towards a Mesh-Independent and User-Independent CFD W.G. Habashi, et al. Artificial Boundary Conditions for Infinite-Domain Problems S.V.Tsynkov. Issues and Strategies for Hyperbolic Problems with Stiff Source Terms M. Arora, P.L. Roe. III: Discontinuities. Numerical Methods for a One-Dimensional Interface Separating Compressible and Incompressible Flows R. Fedkiw, et al. On Some Outstanding Issues in CFD (1996) R. Lohner. Accurate and Robust Methods for Variable Density Incompressible Flows with Discontinuities W.J. Rider, et al. A Variational Approach to Deriving Smeared-Interface Surface Tension Models D. Jacqmin. IV: Other Applications. Compounded of Many Simples: Reflections on the Role of Model Problems in CFD P. Roe. A Unified CFD-Based Approach to a Variety of Problems in Computational Physics R.K. Agarwal. Second Order Godunov Schemes for 2D and 3D MHD Equations and Divergence-Free Condition Wenlong Dai, P.R. Woodward. On Multidimensional Positively Conservative High-Resolution Schemes T. Linde, P.L. Roe. A New Scheme for the Solutions of Multidimensional MHD Equations N. Aslan, T. Kamash . V: Convergence. Local Preconditioning: Who Needs It? B. Van Leer. The Quest for Diagonalization of Differential Systems P. Roe, E. Turkel. Multidimensional Upwinding: Unfolding the Mystery D. Sidilkover.

Transition à la turbulence d'une couche de mélange supersonique

Numerical simulations are used to study the transition to turbulence of a spatially developed compressible mixing layer between rigid walls. The fast and slow flows are supersonic with Mach numbers M 1 = 4.5 and M 2= 1.6 respectively. The full Navier-Stokes equations are solved for a 2D compressible flow with a high order Godunov 's scheme piecewise parabolic method (PPM) with the approximate Riemann solver of Roe. The purpose is to study the transition to turbulence from the linear regime of instability, with comparison to the linear stability analysis of Tam and Hu.

Cross flow tensors and finite volume approximation with by deferred correction

A general framework for full tensor finite volume schemes is presented along with properties of the schemes that in turn provide motivation for a deferred correction scheme. The approach is illustrated by writing a general nine node discretization as a five-node scheme plus a residual term involving the extra nodes. A possible solution procedure involves solving the standard five-node matrix problem to yield an initial solution, then re-solving the problem with the residual determined by the first iterate of the pressure field, relaxation using the pressure from the previous IMPES time step is also examined. Stability of the inner iteration is considered and strategies are discussed. This method is coupled with a higher order Godunov scheme for integrating the convective components of the flow equations. Results presented include two phase flow examples with full tensor fields and serve to demonstrate the potential of the method.

A Second-Order Unsplit Godunov Scheme for Two- and Three-Dimensional Euler Equations

A second-order finite difference scheme is presented in this paper for two- and three-dimensional Euler equations. The scheme is based on nondirectionally split and single-step Eulerian formulations of Godunov approach. A new approach is proposed for constructing effective left and right states of Riemann problems arising from interfaces of one-, two-, and three-dimensional numerical grids. The Riemann problems are solved through an approximate solver in order to calculate a set of time-averaged fluxes needed in the scheme. The scheme is tested through numerical examples involving strong shocks. It is shown that the scheme offers the principle advantages of a second order Godunov scheme: robust operation in the presence of strong waves and thin shock fronts.

Higher order Godunov schemes for isothermal hydrodynamics

In this paper we construct higher order Godunov schemes for isothermal flow. Isothermal hydrodynamics serves as a good representation for several systems of astrophysical interest. The schemes designed here have second-order accuracy in space and time and some are third-order accurate for advection. Moreover, several ingredients of these schemes are essential components of even higher order. The methods designed here have excellent ability to represent smooth flow yet capture shocks with high resolution. Several test problems are presented. The algorithms presented here are compared with other algorithms having a comparable formal order of accuracy.

Turbulent supersonic convection in three dimensions

Previous numerical calculations of two-dimensional, compressible convection are extended to three dimensions, using a higher order Godunov scheme. The results show that the flow readily becomes supersonic in the upper boundary layer, where shock structures form intermittently in the vicinity of the strong downflow lanes. The convection as a whole is strongly time-dependent and evolves on a time scale comparable to the sound crossing time. The motions in the upper layers are characterized by the rapid expansion of the upward-moving fluid elements. In the interior, most of the heat is carried by a small fraction of the fluid residing in strong, highly coherent downflows. The remaining fluid is dominated by small-scale, disorganized turbulent motions.