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Semi-implicit second order schemes for numerical solution of level set advection equation on Cartesian grids

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  • Frolkovič, Peter
  • Mikula, Karol

Abstract

A new parametric class of semi-implicit numerical schemes for a level set advection equation on Cartesian grids is derived and analyzed. An accuracy and a stability study is provided for a linear advection equation with a variable velocity using partial Lax–Wendroff procedure and numerical von Neumann stability analysis. The obtained semi-implicit κ-scheme is 2nd order accurate in space and time in any dimensional case when using a dimension by dimension extension of the one-dimensional scheme that is not the case for analogous fully explicit or fully implicit κ-schemes. A further improvement is obtained by using so-called Corner Transport Upwind extension in two-dimensional case. The extended semi-implicit κ-scheme with a specific (velocity dependent) value of κ is 3rd order accurate in space and time for a constant advection velocity, and it is unconditional stable according to the numerical von Neumann stability analysis for the linear advection equation in general.

Suggested Citation

  • Frolkovič, Peter & Mikula, Karol, 2018. "Semi-implicit second order schemes for numerical solution of level set advection equation on Cartesian grids," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 129-142.
    • Handle: RePEc:eee:apmaco:v:329:y:2018:i:c:p:129-142
    DOI: 10.1016/j.amc.2018.01.065
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    Cited by:

    1. Frolkovič, Peter & Gajdošová, Nikola, 2024. "Unconditionally stable higher order semi-implicit level set method for advection equations," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    2. Frolkovič, Peter & Žeravý, Michal, 2023. "High resolution compact implicit numerical scheme for conservation laws," Applied Mathematics and Computation, Elsevier, vol. 442(C).

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