6533b857fe1ef96bd12b429e

RESEARCH PRODUCT

Trial Methods for Nonlinear Bernoulli Problem

Timo TiihonenKari T. Karkkainen

subject

Bernoulli's principleMathematical optimizationFlow (mathematics)Fixed-point iterationFree boundary problemApplied mathematicsBoundary (topology)Shape optimizationBoundary value problemFixed pointMathematics

description

In this article we consider a free boundary problem which is related to formation of waves on a fluid surface (for example the ship waves). We study the possibility to construct ‘trial’ methods where one solves a sequence of standard flow problems formulated in different geometries that converge to the final free boundary. Furthermore, we use the shape optimization techniques to analyse the convergence of the fixed point iteration near a fixed point. For stream function case we conclude that the fast convergence can be obtained by using non-standard boundary conditions and we present numerical results to confirm the analysis.

yearjournalcountryeditionlanguage
1997-01-01
https://doi.org/10.1007/978-3-322-96688-9_29