A boundary integral equation approach to computing eigenvalues of the Stokes operator
| Autor: | Travis Askham, Manas Rachh |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Discretization
Applied Mathematics Mathematical analysis Fredholm determinant 34B09 31A10 010103 numerical & computational mathematics Numerical Analysis (math.NA) Stokes flow Eigenfunction 01 natural sciences Integral equation 010101 applied mathematics Mathematics - Spectral Theory Computational Mathematics Mathematics - Analysis of PDEs FOS: Mathematics Uniqueness Mathematics - Numerical Analysis 0101 mathematics Stokes operator Spectral Theory (math.SP) Eigenvalues and eigenvectors Mathematics Analysis of PDEs (math.AP) |
| Popis: | The eigenvalues and eigenfunctions of the Stokes operator have been the subject of intense analytical investigation and have applications in the study and simulation of the Navier-Stokes equations. As the Stokes operator is a fourth-order operator, computing these eigenvalues and the corresponding eigenfunctions is a challenging task, particularly in complex geometries and at high frequencies. The boundary integral equation (BIE) framework provides robust and scalable eigenvalue computations due to (a) the reduction in the dimension of the problem to be discretized and (b) the absence of high frequency "pollution" when using a Green's function to represent propagating waves. In this paper, we detail the theoretical justification for a BIE approach to the Stokes eigenvalue problem on simply and multiply-connected planar domains, which entails a treatment of the uniqueness theory for oscillatory Stokes equations on exterior domains. Then, using well-established techniques for discretizing BIEs, we present numerical results which confirm the analytical claims of the paper and demonstrate the efficiency of the overall approach. 38 pages, 12 figures |
| Databáze: | OpenAIRE |
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