Progressive Development of Moving-Grid Finite-Volume Method for Three-Dimensional Incompressible Flows

A finite-volume method is presented for calculating incompressible 3-D flows with curved irregular boundaries. The method employs structured nonorthogonal grids, cell-centered variable arrangement, and Cartesian velocity components. A special interpolation procedure for evaluating the mass fluxes at the cell-faces is used to avoid the nonphysical oscillation of flow variables usually encountered with the cell-centered arrangement. The SIMPLE algorithm is used to handle the pressure-velocity coupling. A recently proposed low diffusive and bounded scheme is introduced to approximate the convection terms in the transport equations. The computer code and the relevant data structure are so organized that most of the code except the implicit linear solver used is fully vectorizable so as to exploit the potential of modern vector computers. The capabilities of the numerical procedure are demonstrated by application to a few internal and external three-dimensional laminar flows. In all cases the CPU-time on a grid with typically 28,000 grid nodes was below half a minute.

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Study of three-dimensional air gun bubble pulsation and the surrounding fluid pressure with finite volume method

Ocean Engineering ◽

10.1016/j.oceaneng.2020.108500 ◽

2021 ◽

Vol 221 ◽

pp. 108500

Author(s):

S. Zhang ◽

B.C. Khoo ◽

A.-M. Zhang

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Fluid Pressure ◽

Three Dimensional ◽

Air Gun ◽

Bubble Pulsation ◽

Volume Method ◽

Surrounding Fluid

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An Unstructured Finite Volume Method for Incompressible Flows With Complex Immersed Boundaries

Volume 13: New Developments in Simulation Methods and Software for Engineering Applications; Safety Engineering, Risk Analysis and Reliability Methods; Transportation Systems ◽

10.1115/imece2009-12917 ◽

2009 ◽

Cited By ~ 2

Author(s):

Lin Sun ◽

Sanjay R. Mathur ◽

Jayathi Y. Murthy

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Incompressible Flows ◽

Simple Algorithm ◽

Flow Region ◽

Solid Material ◽

The Body ◽

Immersed Boundary ◽

Material Points ◽

Volume Method

A numerical method is developed for solving the 3D, unsteady, incompressible flows with immersed moving solids of arbitrary geometrical complexity. A co-located (non-staggered) finite volume method is employed to solve the Navier-Stokes governing equations for flow region using arbitrary convex polyhedral meshes. The solid region is represented by a set of material points with known position and velocity. Faces in the flow region located in the immediate vicinity of the solid body are marked as immersed boundary (IB) faces. At every instant in time, the influence of the body on the flow is accounted for by reconstructing implicitly the velocity the IB faces from a stencil of fluid cells and solid material points. Specific numerical issues related to the non-staggered formulation are addressed, including the specification of face mass fluxes, and corrections to the continuity equation to ensure overall mass balance. Incorporation of this immersed boundary technique within the framework of the SIMPLE algorithm is described. Canonical test cases of laminar flow around stationary and moving spheres and cylinders are used to verify the implementation. Mesh convergence tests are carried out. The simulation results are shown to agree well with experiments for the case of micro-cantilevers vibrating in a viscous fluid.

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