Computational Aeroacoustics: A Wave Number Approach by Christopher K. W. Tam

By Christopher K. W. Tam

Computational Aeroacoustics (CAA) is a comparatively new learn zone. CAA algorithms have constructed quickly and the tools were utilized in lots of components of aeroacoustics. the target of CAA isn't really just to enhance computational equipment but in addition to take advantage of those the right way to remedy sensible aeroacoustics difficulties and to accomplish numerical simulation of aeroacoustic phenomena. through interpreting the simulation facts, an investigator can make certain noise new release mechanisms and sound propagation strategies. this can be either a textbook for graduate scholars and a reference for researchers in CAA and as such is self-contained. No previous wisdom of numerical equipment for fixing PDE's is required, even if, a normal realizing of partial differential equations and easy numerical research is thought. routines are incorporated and are designed to be an essential component of the bankruptcy content material. moreover, pattern computing device courses are integrated to demonstrate the implementation of the numerical algorithms.

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Computational Aeroacoustics: A Wave Number Approach

Computational Aeroacoustics (CAA) is a comparatively new study quarter. CAA algorithms have constructed swiftly and the equipment were utilized in lots of parts of aeroacoustics. the target of CAA isn't really just to improve computational equipment but in addition to exploit those the way to clear up sensible aeroacoustics difficulties and to accomplish numerical simulation of aeroacoustic phenomena.

Extra resources for Computational Aeroacoustics: A Wave Number Approach

Example text

This is because x = ω′ (α) t so that α is a constant along a given line (ray) x/t = constant. 1. (a) Rays of x = ω′ (α)t for constant α in the x–t diagram. (b) Initial energy spectrum. Furthermore, dx/dt = ω′ (α), suggesting that ω′ (α), the group velocity, is the speed of propagation of wave number α. 2. Far away, the waves may be regarded as initiated locally near x = 0. 1a. A quantity of interest in wave propagation is the wave energy that is |A|2 = AA* (* denotes the complex conjugate). 1a) is x1 (t ) x1 (t ) ∗ Q(t ) = AA dx = x2 (t ) x2 (t ) 1 H(α, ω) ∂D 2π ∂ω 2 1 dx.

The poles are given by the zeros of the denominator of the integrand, that is, the roots of ω(ω) = cα(α). 20) Eq. 20) is the dispersion relation. , Eq. 14), provided ω is replaced by ω and α is replaced by α. For this reason, the finite difference scheme is referred to as dispersion-relation-preserving (DRP). For a four-level time marching scheme, there would be four poles or Eq. 20) has four roots. Let the poles be ω = ω j (α), j = 1, 2, 3, 4. One of the poles has Im(ω) nearly equal to zero. This is the pole that corresponds to the physical solution.

Dispersion-relation-preserving scheme is the optimized scheme, · · · · · · · exact solution, ——— computed solution. 9. With b ≥ 2, the optimized scheme gives good waveform. However, for an extremely narrow pulse, b = 1, none of these schemes can provide a solution free of spurious waves. 5 Backward Difference Stencils Near the boundary of a computation domain, a symmetric stencil cannot be used; backward difference stencils are needed. 10 shows the various 7-point backward difference stencils. Unlike symmetric stencil, the wave number of a backward difference stencil is complex.

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