Aero-acoustics and noise
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==Higher Order Schemes for Aero-acoustics== | ==Higher Order Schemes for Aero-acoustics== | ||
=== Necessity === | === Necessity === | ||
| - | Acoustic problems are governed by the linearised Euler equation and it is known from wave propagation theory that the propagation characteristics of waves governed by a system of partial different equations are encoded in the dispersion relation. | + | Acoustic problems are governed by the linearised Euler equation and it is known from wave propagation theory that the propagation characteristics of waves governed by a system of partial different equations are encoded in the dispersion relation.The dispersion relation of a system of equation can be used to determine the isotropy,group and phase velocities of all kinds of waves supported by the system of equations.With this idea in mind it is clear that we need a finite difference scheme which has almost similar dispersion relation to the original system of equations.It is well known that the first order schemes lead to excessive dissipation error and second order schemes have a lot of dispersion errors.This motivated the study to develop a class of finite difference schemes which can be suited to the modelling of wave propagation problems.This class of finite difference schemes are usually referred to as dispersion relation preserving schemes ( DRP Schemes ). |
| + | === Construction of DRP Schemes === | ||
| + | === Stability === | ||
| + | === Implementation == | ||
Revision as of 23:55, 13 October 2005
Contents |
Higher Order Schemes for Aero-acoustics
Necessity
Acoustic problems are governed by the linearised Euler equation and it is known from wave propagation theory that the propagation characteristics of waves governed by a system of partial different equations are encoded in the dispersion relation.The dispersion relation of a system of equation can be used to determine the isotropy,group and phase velocities of all kinds of waves supported by the system of equations.With this idea in mind it is clear that we need a finite difference scheme which has almost similar dispersion relation to the original system of equations.It is well known that the first order schemes lead to excessive dissipation error and second order schemes have a lot of dispersion errors.This motivated the study to develop a class of finite difference schemes which can be suited to the modelling of wave propagation problems.This class of finite difference schemes are usually referred to as dispersion relation preserving schemes ( DRP Schemes ).
