Numerical solution of compressible viscous flows at high Reynolds numbers

A new numerical method which was used to reduce the computation time required in fluid dynamics to solve the Navier-Stokes equations at flight Reynolds numbers is described. The method is the implicit analogue of the explicit finite different method. It uses this as its first stage, while the second stage removes the restrictive stability condition by recasting the difference equations in an implicit form. The resulting matrix equations to be solved are either upper or lower block bidiagonal equations. The new method makes it possible and practical to calculate many important three dimensional, high Reynolds number flow fields on computers

An LU implicity scheme for high speed inlet analysis

A numerical method is developed to analyze the inviscid flowfield of a high speed inlet by the solution of the Euler equations. The lower-upper implicit scheme in conjunction with adaptive dissipation proves to be an efficient and robust nonoscillatory shock capturing technique for high Mach number flows as well as for transonic flows

Some observations on a new numerical method for solving Navier-Stokes equations

An explicit-implicit technique for solving Navier-Stokes equations is described which, is much less complex than other implicit methods. It is used to solve a complex, two-dimensional, steady-state, supersonic-flow problem. The computational efficiency of the method and the quality of the solution obtained from it at high Courant-Friedrich-Lewy (CFL) numbers are discussed. Modifications are discussed and certain observations are made about the method which may be helpful in using it successfully

Comparison of Various Numerical Techniques in Gas Dynamics

In search of reliable numerical methods for gas dynamic flow problems, we apply the MacCormack method algorithm and two new algorithms to two representative problems in gas dynamics. The MacCormack method, which is most commonly employed in aerodynaics, proves to be good for the time developing problem. The explicit Satofuka method, which is claimed to be stable even if the CFL condition is violated, turns out to be rather inaccurate for a problem with a CFL number larger than unity. We find that the New MacCormack implicit method is suitable for the time steady problem

Multi-stage high order semi-Lagrangian schemes for incompressible flows in Cartesian geometries

Efficient transport algorithms are essential to the numerical resolution of incompressible fluid flow problems. Semi-Lagrangian methods are widely used in grid based methods to achieve this aim. The accuracy of the interpolation strategy then determines the properties of the scheme. We introduce a simple multi-stage procedure which can easily be used to increase the order of accuracy of a code based on multi-linear interpolations. This approach is an extension of a corrective algorithm introduced by Dupont \& Liu (2003, 2007). This multi-stage procedure can be easily implemented in existing parallel codes using a domain decomposition strategy, as the communications pattern is identical to that of the multi-linear scheme. We show how a combination of a forward and backward error correction can provide a third-order accurate scheme, thus significantly reducing diffusive effects while retaining a non-dispersive leading error term.Comment: 14 pages, 10 figure

A new numerical framework for solving conservation laws: The method of space-time conservation element and solution element

A new numerical framework for solving conservation laws is being developed. It employs: (1) a nontraditional formulation of the conservation laws in which space and time are treated on the same footing, and (2) a nontraditional use of discrete variables such as numerical marching can be carried out by using a set of relations that represents both local and global flux conservation