TY  - JOUR
A1  - Höllbacher, Susanne
A1  - Wittum, Gabriel
T1  - Rotational test spaces for a fully-implicit FVM and FEM for the DNS of fluid-particle interaction
T2  - Journal of computational physics
N2  - The paper presents a fully-implicit and stable finite element and finite volume scheme for the simulation of freely moving particles in a fluid. The developed method is based on the Petrov-Galerkin formulation of a vertex-centered finite volume method (PG-FVM) on unstructured grids. Appropriate extension of the ansatz and test spaces lead to a formulation comparable to a fictitious domain formulation. The purpose of this work is to introduce a new concept of numerical modeling reducing the mathematical overhead which many other methods require. It exploits the identification of the PG-FVM with a corresponding finite element bilinear form. The surface integrals of the finite volume scheme enable a natural incorporation of the interface forces purely based on the original bilinear operator for the fluid. As a result, there is no need to expand the system of equations to a saddle-point problem. Like for fictitious domain methods the extended scheme treats the particles as rigid parts of the fluid. The distinguishing feature compared to most existing fictitious domain methods is that there is no need for an additional Lagrange multiplier or other artificial external forces for the fluid-solid coupling. Consequently, only one single solve for the derived linear system for the fluid together with the particles is necessary and the proposed method does not require any fractional time stepping scheme to balance the interaction forces between fluid and particles. For the linear Stokes problem we will prove the stability of both schemes. Moreover, for the stationary case the conservation of mass and momentum is not violated by the extended scheme, i.e. conservativity is accomplished within the range of the underlying, unconstrained discretization scheme. The scheme is applicable for problems in two and three dimensions.
KW  - Non-Lagrange multiplier method
KW  - Strong coupling
KW  - Fictitious domain
KW  - Fluid-particle interaction
KW  - Petrov-Galerkin finite volumes
KW  - Finite elements
Y1  - 2019
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/77604
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-776046
SN  - 0021-9991
VL  - 393
SP  - 186
EP  - 213
PB  - Elsevier
CY  - Amsterdam
ER  -