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Fully discrete energy stable high order finite difference methods for hyperbolic problems in deforming domainsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2015 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 291, p. 82-98Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier , 2015. Vol. 291, p. 82-98
##### Keyword [en]

Deforming domain; Initial boundary value problems; High order accuracy; Well-posed boundary conditions; Summation-by-parts operators; Stability; Convergence; Conservation; Numerical geometric conservation law; Euler equation; Sound propagation
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:liu:diva-117360DOI: 10.1016/j.jcp.2015.02.027ISI: 000352230500006OAI: oai:DiVA.org:liu-117360DiVA, id: diva2:807873
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Available from: 2015-04-24 Created: 2015-04-24 Last updated: 2017-12-04
##### In thesis

A time-dependent coordinate transformation of a constant coefficient hyperbolic system of equations which results in a variable coefficient system of equations is considered. By applying the energy method, well-posed boundary conditions for the continuous problem are derived. Summation-by-Parts (SBP) operators for the space and time discretization, together with a weak imposition of boundary and initial conditions using Simultaneously Approximation Terms (SATs) lead to a provable fully-discrete energy-stable conservative finite difference scheme. We show how to construct a time-dependent SAT formulation that automatically imposes boundary conditions, when and where they are required. We also prove that a uniform flow field is preserved, i.e. the Numerical Geometric Conservation Law (NGCL) holds automatically by using SBP-SAT in time and space. The developed technique is illustrated by considering an application using the linearized Euler equations: the sound generated by moving boundaries. Numerical calculations corroborate the stability and accuracy of the new fully discrete approximations.

1. Stable High Order Finite Difference Methods for Wave Propagation and Flow Problems on Deforming Domains$(function(){PrimeFaces.cw("OverlayPanel","overlay956877",{id:"formSmash:j_idt705:0:j_idt709",widgetVar:"overlay956877",target:"formSmash:j_idt705:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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