/pdf/asymptotic-analysis-of-periodic-structures-14wjonu4ba.pdf

Asymptotic Analysis of Periodic Structures

A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used to determine the steady transonic flow past an airfoil using an O mesh. Convergence to a steady state is accelerated by the use of a variable time step determined by the local Courant member, and the introduction of a forcing term proportional to the difference between the local total enthalpy and its free stream value.

Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes

Boundary conditions for direct simulations of compressible viscous flows

In practical calculations, it is often essential to introduce artificial boundaries to limit the area of computation. Here we develop a systematic method for obtaining a hierarchy of local boundary conditions at these artifical boundaries. These boundary conditions not only guarantee stable difference approximations, but also minimize the (unphysical) artificial reflections that occur at the boundaries.

/pdf/absorbing-boundary-conditions-for-the-numerical-simulation-4ptpuyjckz.pdf

Absorbing boundary conditions for the numerical simulation of waves

Fully multidimensional flux-corrected transport algorithms for fluids

Initial boundary value problems for hyperbolic systems

Historically, second order accurate difference methods have been used for computations in dynamic meteorology and oceanography. We investigate more accurate difference methods and show that fourth order methods are optimal in some sense. This method is then compared with a variant of the Fourier technique. DOI: 10.1111/j.2153-3490.1972.tb01547.x

Comparison of accurate methods for the integration of hyperbolic equations

Publisher Summary
This chapter defines finite element and finite difference methods for hyperbolic partial differential equations. The advantage of the finite element method is that the resulting procedures are automatically stable and there is extreme flexibility in choosing the basic functions. Therefore, in very complicated domains or for problems with complicated interfaces, the method is the only feasible one. For hyperbolic partial differential equations it is essential to control the dispersion, dissipation, and the propagation of discontinuities. This is easily done by using suitable difference approximations. The main disadvantage of finite difference methods is that it may be difficult to handle boundaries properly.

Finite Element and Finite Difference Methods for Hyperbolic Partial Differential Equations

Boundary Conditions for Time Dependent Problems with an Artificial Boundary

We consider difference methods for the solution of singular perturbations of boundary value problems. The solutions are smooth except in boundary layers of thickness ?|log?|, 0<??1. Various difference schemes with a uniform stepsizeh are considered. In practice,h is usually much larger than the boundary layer regions. Then the difference methods must be choosen with care. It is shown that only approximations of low order accuracy can be used. However, one can increase the accuracy by a Richardson procedure. Asymptotic expansions in powers ofh and ? are given for the solutions of the proposed methods.

Heinz-Otto Kreiss

Papers

Initial boundary value problems for hyperbolic systems

Comparison of accurate methods for the integration of hyperbolic equations

Finite Element and Finite Difference Methods for Hyperbolic Partial Differential Equations

Boundary Conditions for Time Dependent Problems with an Artificial Boundary

Difference approximations for singular perturbations of systems of ordinary differential equations