 Semi-implicit second order schemes for numerical solution of level set advection equation on Cartesian gridsPeter Frolkovič and Karol Mikula Applied Mathematics and Computation, 2018, vol. 329, issue C, 129-142 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. Keywords: Advection equation; Finite difference method; Cartesian grid; Lax–Wendroff procedure; von Neumann stability analysis (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:329:y:2018:i:c:p:129-142 DOI: 10.1016/j.amc.2018.01.065 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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