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

Semi-implicit second order schemes for numerical solution of level set advection equation on... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Computation Elsevier

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

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Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier Inc.
ISSN
0096-3003
eISSN
1873-5649
D.O.I.
10.1016/j.amc.2018.01.065
Publisher site
See Article on Publisher Site

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.

Journal

Applied Mathematics and ComputationElsevier

Published: Jul 15, 2018

References

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