1996/05/01 by Jae Wook Kim, Duck Joo Lee · 4 citations
Earth and Planetary Sciences · Engineering · Environmental Science · #Meteorological Phenomena and Simulations #Computational Fluid Dynamics and Aerodynamics #Wind and Air Flow Studies
paper · doi:10.2514/3.13164
Direct numerical simulations and computational aeroacoustics require an accurate finite difference scheme that has a high order of truncation and high-resolution characteristics in the evaluation of spatial derivatives. Compact finite difference schemes are optimized to obtain maximum resolution characteristics in space for various spatial truncation orders. An analytic method with a systematic procedure to achieve maximum resolution characteristics is devised for multidiagonal schemes, based on the idea of the minimization of dispersive (phase) errors in the wave number domain, and these are applied to the analytic optimization of multidiagonal compact schemes. Actual performances of the optimized compact schemes with a variety of truncation orders are compared by means of numerical simulations of simple wave convections, and in this way the most effective compact schemes are found for tridiagonal and pentadiagonal cases, respectively. From these comparisons, the usefulness of an optimized high-order tridiagonal compact scheme that is more efficient than a pentadiagonal scheme is discussed. For the optimized high-order spatial schemes, the feasibility of using classical high-order Runge-Kutta time advancing methods is investigated. Nomenclature a, b, c = coefficients of compact discretization to be optimized E = integrated error of compact discretization in point of wave number range e = resolving efficiency / = objective function / ' = spatial derivative of objective function / = Fourier transformed objective function r- optimization range factor W = weighting function for optimization of coefficients a, ft = coefficients of compact discretization to be optimized s = error tolerance K = scaled true wave number K = scaled modified wave number Kf = scaled critical wave number co = true wave number cb = modified wave number a)f = critical wave number