Pressure-Based Residual Smoothing Operators for Multistage Pseudocompressibility Algorithms
✍ Scribed by F. Sotiropoulos; G. Constantinescu
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 591 KB
- Volume
- 133
- Category
- Article
- ISSN
- 0021-9991
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✦ Synopsis
Implicit residual smoothing operators for accelerating the convergence of explicit, multistage, artificial compressibility algo-overhead (typically less than 10% of the total CPU time rithms are developed using ideas from pressure-based methods. per iteration) since only inversions of scalar tridiagonal
The velocity derivatives in the continuity equation and the pressure matrices are required.
gradient terms in the momentum equations are discretized in The objective of this paper is to exploit certain properties time implicitly. The discrete system of equations is linearized in of the incompressible flow equations to develop a residual time producing a block implicit operator which is approximately factorized and diagonalized via a similarity transformation. The smoothing operator, specifically tailored for explicit, so-derived diagonal operator depends only on the metrics of the multistage AC algorithms. Such an operator must exhibit geometric transformation and can, thus, be implemented in an the simplicity and computational efficiency of the standard efficient and straightforward manner. It is combined with the IRS operator and further enhance the damping of highstandard implicit residual smoothing operator and incorporated frequency errors, so that it can be used as an effective in a four-stage Runge-Kutta algorithm also enhanced with local time-stepping and multigrid acceleration. Linear stability analysis multigrid smoother for incompressible flow solutions. To for the three-dimensional Navier-Stokes equations and calculaconstruct such an operator, we explore the possibility of tions for laminar flows through curved square ducts and pipes combining ideas from pressure-based, or pressure-Poisson demonstrate the damping properties and efficiency of the pro-(PP), methods with pseudo-compressible formulations.
posed approach particularly on large-aspect ratio, highly skewed Consider a PP method in which the momentum equations meshes. ᮊ 1997 Academic Press are advanced in time explicitly [1][2][3]. In such an algorithm the velocity derivatives in the continuity equation and the pressure gradient terms in momentum equations are dis-