Comparison of two solution strategies for use with higher‐order discretization schemes in fluid flow simulation

Gaskell, Philip; Lau, A. K. C.; Wright, Nigel

doi:10.1002/fld.1650081008

Cited by 21 publications

(8 citation statements)

References 17 publications

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“…The solution of this equation is of the same form as equation (14), with PA replaced by PX. But this can be forced to match the true solution, equation (16), by setting giving, on rearrangement, an explicit formula for the effective grid Peclet number in terms of the…”

Section: -1mentioning

confidence: 99%

Beyond first‐order upwinding: The ultra‐sharp alternative for non‐oscillatory steady‐state simulation of convection

Leonard¹,

Mokhtari²

1990

Numerical Meth Engineering

238

140

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SUMMARYAlthough it is now well known that first-order convection schemes suffer from serious inaccuracies attributable to artificial viscosity or numerical diffusion under high-convection conditions, these methods continue to enjoy widespread popularity for numerical heat-transfer calculations, apparently owing to a perceived lack of viable high-accuracy alternatives. But alternatives are available. For example, nonoscillatory methods used in gasdynamics, including currently popular 'TVD schemes, can be easily adapted to multidimensional incompressible flow and convective transport. This, in itself, would be a major advance for numerical convective heat transfer, for example. But, as this paper shows, second-order TVD schemes form only a small, overly restrictive, subclass of a much more universal, and extremely simple, nonoscillatory flux-limiting strategy which can be applied to convection schemes of arbitrarily high-order accuracy, while requiring only a simple tridiagonal AD1 line-solver, as used in the majority of generalpurpose iterative codes for incompressible flow and numerical heat transfer. The new universal limiter and associated solution procedures form the so-called ULTRA-SHARP alternative for high-resolution nonoscillatory multidimensional steady-state high-speed convective modelling.

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Section: -1mentioning

confidence: 99%

Beyond first‐order upwinding: The ultra‐sharp alternative for non‐oscillatory steady‐state simulation of convection

Leonard¹,

Mokhtari²

1990

Numerical Meth Engineering

238

140

View full text Add to dashboard Cite

show abstract

“…The components of the body force f are f x = 0 and f y = gb T -T 0 ( ), where b = -1 r qr qT is the thermal volumetric expansion coe cient. Staggered meshes [7] and SMART [26] (implemented with the deferred correction procedure [27]) are used.…”

Section: Governing Equat Ions and Num Erical Aspect Smentioning

confidence: 99%

A Direct Parallel Algorithm for the Efficient Solution of the Pressure-Correction Equation of Incompressible Flow Problems Using Loosely Coupled Computers

Sòria¹,

Segarra²,

Oliva³

2002

Numerical Heat Transfer, Part B: Fundamentals

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The numerical simulation of time-accurated complex ows needs large computational resources. For the case of incompressible ows, the solution of the pressure-correction equation is typically the main bottleneck, especially on loosely coupled parallel computers such as PC clusters. An algorithm intended to solve this problem is presented. It is a variant of the Schur complement method that uses direct solvers for each subdomain and for the interface equation. The inverse of the interface matrix is evaluated and stored in parallel. Simulation of turbulent natural convection is used as a benchmark to show its potential and limitations.

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“…Another application of the method is in multigrid calculations. The conflicting demand for a smooth error field and for global mass conservation at boundaries seriously limits the application of multigrid methods to flow with open boundaries, (Gaskell and Lau (1988); Sockol (1993». It is well-known that local correction of the free boundary flow rate is detrimental to multigrid acceleration, (Brandt (1984».…”

Section: Introductionmentioning

confidence: 99%

A Distributive Mass Balance Correction in Single- and Multigrid Incompressible Flow Calculation

Zeng

Matovic

Pollard

et al. 1996

International Journal of Computational Fluid Dynamics

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The pressure-velocity coupling in a finite volume method (SIMPLE-type) is enhanced usinga distributed mass balance correction method.The mass imbalancegenerated by the momentum equations isdistributed over all control volumesprior to solvingthe pressurecorrection equation. This method considerablyenhances the convergenceof the SIMPLE method, whether used on either a single staggered grid or a collocated multigrid. Some simple two-and three-dimensional laminar flows are used to test the method.

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Comparison of two solution strategies for use with higher‐order discretization schemes in fluid flow simulation

Cited by 21 publications

References 17 publications

Beyond first‐order upwinding: The ultra‐sharp alternative for non‐oscillatory steady‐state simulation of convection

Beyond first‐order upwinding: The ultra‐sharp alternative for non‐oscillatory steady‐state simulation of convection

A Direct Parallel Algorithm for the Efficient Solution of the Pressure-Correction Equation of Incompressible Flow Problems Using Loosely Coupled Computers

A Distributive Mass Balance Correction in Single- and Multigrid Incompressible Flow Calculation

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