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Cartesian Mesh-based Incompressible Flow Simulation over Arbitrarily Complex Geometries using a Multigrid Method

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Abstract
In this dissertation, two algorithms for efficient Cartesian mesh-based flow simulations over
arbitrarily complex objects are presented. As a first category of this dissertation, a geometric
multigrid (MG) algorithm using the Heaviside function restriction is presented. This algorithm
is simple to implement, readily parallelizable, and can be applied to any irregular domain
problem. The validity of the presented algorithm is demonstrated by solving an analytically
defined Poisson problem on an irregular domain. Furthermore, the optimal performance of the
MG method is also demonstrated herein. As a second category of this dissertation, a novel
efficient and reliable determination procedure of the signed distance function (SDF) based on
an adaptive mesh refinement (AMR) strategy is described. Our motivation is that the SDF near
the solid boundary is accurately required in the fluid simulation, whereas the SDF of the rest
region can be considered as arbitrarily large values if the sign is correct. We employ the AMR
procedure in order to efficiently define interface cells containing the solid boundary. By
focusing on interface cells in hierarchical grids, the number of operations for computing the
SDF can be reduced significantly. The efficiency and accuracy of the proposed method is
demonstrated by volume convergence tests.
By combining above two algorithms with an existing solution algorithm for the fluid, an inhouse
Cartesian mesh-based incompressible flow solver is developed. The hybrid
MPI/OpenMP parallelization is applied to this solver, and parallel computation is conducted
on the KISTI`s Nurion supercomputer. To demonstrate applicability of the current approach,
various well-known benchmark problems in both 2D and 3D are simulated, and all results are
validated with previous experimental and numerical data. Furthermore, as the most challenging
test case, simulations for flow over an underwater walking robot, namely Crabster, are
presented. Finally, golf ball wake simulations with and without back-spin are presented as a
very large-scale problem, which consists of ten-billions order cells.
Author(s)
고광수
Issued Date
2019
Awarded Date
2019-08
Type
Dissertation
Keyword
MultigridSigned Distance Function (SDF)Complex GeometryIncompressible FlowCartesian Grid
URI
https://oak.ulsan.ac.kr/handle/2021.oak/6168
http://ulsan.dcollection.net/common/orgView/200000221038
Alternative Author(s)
Gwangsoo Go
Affiliation
울산대학교
Department
일반대학원 조선및해양공학과
Advisor
안형택
Degree
Doctor
Publisher
울산대학교 일반대학원 조선및해양공학과
Language
eng
Rights
울산대학교 논문은 저작권에 의해 보호받습니다.
Appears in Collections:
Ship Building & Marine Engineering > 2. Theses (Ph.D)
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