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International Journal for Uncertainty Quantification
IF: 3.259 5-Year IF: 2.547 SJR: 0.417 SNIP: 0.8 CiteScore™: 1.52

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2019029228
pages 471-492

KERNEL-BASED STOCHASTIC COLLOCATION FOR THE RANDOM TWO-PHASE NAVIER-STOKES EQUATIONS

M. Griebel
Institute for Numerical Simulation, Bonn University, Endenicher Allee 19b, D-53115 Bonn, Germany; Fraunhofer Institute for Algorithms and Scientific Computing SCAI, Schloss Birlinghoven, D-53754 Sankt Augustin, Germany
C. Rieger
Institute for Numerical Simulation, Bonn University, Endenicher Allee 19b, D-53115 Bonn, Germany; Department of Mathematics, RWTH Aachen University, Schinkelstr. 2, D-52062 Aachen, Germany
Peter Zaspel
Department of Mathematics and Computer Science, University of Basel, Spiegelgasse 1, 4051 Basel, Switzerland

ABSTRACT

In this work, we apply stochastic collocation methods with radial kernel basis functions for an uncertainty quantification of the random incompressible two-phase Navier-Stokes equations. Our approach is nonintrusive and we use the existing fluid dynamics solver NaSt3DGPF to solve the incompressible two-phase Navier-Stokes equation for each given realization. We are able to empirically show that the resulting kernel-based stochastic collocation is highly competitive in this setting and even outperforms some other standard methods.

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