Comparison of numerical schemes for solving the advection equation

We report on the dispersion and dissipation properties of numerical schemes aimed at solving the one-dimensional advection equation. The study is based on the consistency error, which is explicitly calculated for various standard finite-difference schemes. The oscillation and damping features of the...

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Bibliographic Details
Published inApplied mathematics letters Vol. 16; no. 2; pp. 147 - 154
Main Authors Bouche, D., Bonnaud, G., Ramos, D.
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 01.02.2003
Elsevier
Subjects
Advection equation
Exact sciences and technology
Mathematical analysis
Mathematics
Numerical schemes
Partial differential equations
Sciences and techniques of general use
Spurious oscillations
Advection equation
Numerical schemes
Spurious oscillations
Generalized function
Consistency
Prediction
Lax Wendroff scheme
Advection diffusion equation
Numerical method
Partial differential equation
Standards
Advection
Vibration damping
Integrated circuit
Hyperbolic equation
Oscillation
Step function
Finite difference method
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Summary:We report on the dispersion and dissipation properties of numerical schemes aimed at solving the one-dimensional advection equation. The study is based on the consistency error, which is explicitly calculated for various standard finite-difference schemes. The oscillation and damping features of the numerical solutions are shown to be explained via a generalized Airy-like function. In the specific case of the advection of a step function, the solutions of the equivalent equations are systematically calculated and shown to recover the numerical solutions. A particular emphasis is put on one third-order accurate scheme, which involves a weak smearing of the step.
ISSN:0893-9659
1873-5452
DOI:10.1016/S0893-9659(03)80024-1