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A super-compact higher order scheme for the unsteady 3D incompressible viscous flows

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Abstract

In this study, we present an implicit super-compact higher order scheme to solve the unsteady three-dimensional Navier–Stokes equations which is second-order accurate in time and fourth-order accurate in space. The stencil requires 19 points at the \(n\mathrm{th}\) time level and only seven points at the \((n+1)\mathrm{th}\) time level. The parabolic momentum equations are solved with a time-marching strategy and the pressure is obtained by a pressure-correction strategy based on a modified artificial compressibility approach. In the process, we also provide a Fourier stability analysis for the proposed scheme along with an analysis on its dispersion and diffusion characteristics. The scheme efficiently captures the solutions of both unsteady and steady-state Navier–Stokes equations: we first apply it to two problems having analytical solutions and then to the unsteady lid-driven cubic cavity problem. Our numerical results are excellent match with the analytical as well as established numerical results for the cavity.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Guwahati, 781 039, India

    Jiten C. Kalita

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  1. Jiten C. Kalita
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Correspondence to Jiten C. Kalita.

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Communicated by Abimael Loula.

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Kalita, J.C. A super-compact higher order scheme for the unsteady 3D incompressible viscous flows. Comp. Appl. Math. 33, 717–738 (2014). https://doi.org/10.1007/s40314-013-0090-y

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  • DOI: https://doi.org/10.1007/s40314-013-0090-y

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