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A Modal PML for the 2D Shallow Water Equations in Conservative Variables
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
2015 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Ett modalt PML för de två-dimensionella ekvationerna för grunt vatten i konservativa variabler (Swedish)
Abstract [en]

A modal Perfectly Matched Layer (PML) is constructed for the two-dimensional, non-linear, Shallow Water Equations (SWEs) in conservative variables. The result is an analytical continuation of the original equations where absorption is applied to the outgoing wave modes which are damped exponentially fast in the direction of propagation. Numerical tests are performed using a variation of the Diagonally Implicit Runge-Kutta (DIRK) integration scheme in conjunction with Lax-Wendroff’s method for smooth so- lutions and some variation of Roe’s method for discontinuous solutions.

Different absorption functions are used, i.e. the absorption function of the original PML constructed by Berenger for electromagnetic waves, and some variations of the hyperbola functions. The results clearly show that the PML is better than the characteristic boundary condition, but also that improvements through some sort of optimization should lead to better parameter choices, potentially decreasing the reflections further.

Abstract [sv]

Ett modalt Perfekt Matchande Lager (PML) konstrueras för de två-dimensionella, icke-linjära, ekvationerna för grunt vatten (Shallow Water-ekvationerna (SWE)) i konservativa variabler. Resultatet är en analytisk fortsättning av de ursprungliga ekvationerna där absorption tillämpas på de utgående vågmoderna som dämpas med exponentiell hastighet i utbredningsriktningen. Numeriska tester genomförs med en version av det Diagonalt Implicita Runge-Kutta (DIRK) schemat tillsammans med Lax-Wendroffs metod för kontinuerliga lösningar och en variant av Roes metod för diskontinuerliga lösningar. Olika absorptionsfunktioner används, d.v.s. absorptionsfunktionen från det ursprungliga PML:et konstruerat av Berenger för elektromagnetiska vågor, samt olika versioner av hyperbola-funktionerna. Resultaten visar tydligt att PML:et är bättre än det karakteristiska randvillkoret, men också att förbättringar genom någon sorts optimering borde leda till bättre parameterval, och potentiellt minska reflektionerna ytterligare.

Place, publisher, year, edition, pages
2015.
Series
TRITA-MAT-E, 2015:83
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-177883OAI: oai:DiVA.org:kth-177883DiVA: diva2:874841
Subject / course
Scientific Computing
Educational program
Master of Science - Scientific Computing
Supervisors
Examiners
Available from: 2015-11-29 Created: 2015-11-29 Last updated: 2016-01-14Bibliographically approved

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CiteExportLink to record
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