On An Equal Fourth-Order-Accurate Temporal/Spatial Scheme for the Convection-Diffusion Equation

Sheu, Tony W. H.; Lin, R. K.

doi:10.1080/10407790600710168

Cited by 5 publications

(1 citation statement)

References 24 publications

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“…In the context of Navier Stokes equations (NSE), the vorticity transport equation (VTE) pertaining to the vorticity-stream function (VS) formulation can be exactly classified as a CDE; whereas, the analogous momentum equations in primitive variable (PV) formulation only resembles the CDE because of the presence of pressure gradient term. It is due to this obvious reason, that developed HOC polynomial [1][2][3][4][5][6][7][8][9][10] and exponential schemes [11] are straightforward in their implementation to the VS formulation. However, the requirement of three-dimensional simulations makes the consideration of extending these schemes to the primitive variable form of UINSE inevitable.…”

Section: Introductionmentioning

confidence: 98%

A Novel Semi-Explicit Spatially Fourth Order Accurate Projection Method for Unsteady Incompressible Viscous Flows

Sekarapandian

Sanyasiraju

Vengadesan

2009

Numerical Heat Transfer, Part A: Applications

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This article describes a simple and elegant compact higher order finite-difference based numerical solution technique to the primitive variable formulation of unsteady incompressible Navier Stokes equations (UINSE) on staggered grids. The method exploits the advantages of the D'yakanov ADI-like scheme and a non-iterative pressure correction based fractional step method. Spatial derivatives are discretized to fourth order accuracy and the time integration is realized through the Euler explicit method. The fast and efficient iterative solution to the discretized momentum and pressure Poisson equations is achieved using a variant of conjugate gradient method. Spatial accuracy and robustness of the solver are tested through its application to relevant benchmark problems.

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