Discrete equivalence of adjoint neumann–dirichlet div-grad and grad-div equations in curvilinear 3d domains

Discrete equivalence of adjoint neumann–dirichlet div-grad and grad-div equations in curvilinear 3d domains

Zhang, Yi (Student TU Delft)
Jain, V. (TU Delft Aerodynamics)
Palha da Silva Clérigo, A. (Eindhoven University of Technology)
Gerritsma, M.I. (TU Delft Aerodynamics)

Sherwin, Spencer J. (editor)
Peiró, Joaquim (editor)
Vincent, Peter E. (editor)
Moxey, David (editor)
Schwab, Christoph (editor)

2020

In this paper, we will show that the equivalence of a div-grad Neumann problem and a grad-div Dirichlet problem can be preserved at the discrete level in 3-dimensional curvilinear domains if algebraic dual polynomial representations are employed. These representations will be introduced. Proof of the equivalence at the discrete level follows from the construction of the algebraic dual representations. A 3-dimensional test problem in curvilinear coordinates will illustrate this approach.

http://resolver.tudelft.nl/uuid:7c6934d8-7940-40e3-9aeb-a992cdd83c04

https://doi.org/10.1007/978-3-030-39647-3_15

SpringerOpen

9783030396466

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference

12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018, 2018-07-09 → 2018-07-13, London, United Kingdom

Lecture Notes in Computational Science and Engineering, 1439-7358, 134

Institutional Repository

conference paper

© 2020 Yi Zhang, V. Jain, A. Palha da Silva Clérigo, M.I. Gerritsma