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Simulation of three‐dimensional incompressible flows in generalized curvilinear coordinates using a high‐order compact finite‐difference lattice Boltzmann method
Author(s) -
Ezzatneshan Eslam,
Hejranfar Kazem
Publication year - 2018
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4693
Subject(s) - curvilinear coordinates , lattice boltzmann methods , mathematics , compact finite difference , discretization , mathematical analysis , finite difference , incompressible flow , finite difference method , boltzmann equation , geometry , flow (mathematics) , physics , mechanics , quantum mechanics
Summary In the present study, a high‐order compact finite‐difference lattice Boltzmann method is applied for accurately computing 3‐D incompressible flows in the generalized curvilinear coordinates to handle practical and realistic geometries with curved boundaries and nonuniform grids. The incompressible form of the 3‐D nineteen discrete velocity lattice Boltzmann method is transformed into the generalized curvilinear coordinates. Herein, a fourth‐order compact finite‐difference scheme and a fourth‐order Runge‐Kutta scheme are used for the discretization of the spatial derivatives and the temporal term, respectively, in the resulting 3‐D nineteen discrete velocity lattice Boltzmann equation to provide an accurate 3‐D incompressible flow solver. A high‐order spectral‐type low‐pass compact filtering technique is applied to have a stable solution. All boundary conditions are implemented based on the solution of the governing equations in the 3‐D generalized curvilinear coordinates. Numerical solutions of different 3‐D benchmark and practical incompressible flow problems are performed to demonstrate the accuracy and performance of the solution methodology presented. Herein, the 2‐D cylindrical Couette flow, the decay of a 3‐D double shear wave, the cubic lid‐driven cavity flow with nonuniform grids, the flow through a square duct with 90° bend and the flow past a sphere at different flow conditions are considered for validating the present computations. Numerical results obtained show the accuracy and robustness of the present solution methodology based on the implementation of the high‐order compact finite‐difference lattice Boltzman method in the generalized curvilinear coordinates for solving 3‐D incompressible flows over practical and realistic geometries.