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High-order weighted essentially nonoscillatory finite-difference formulation of the lattice boltzmann method in generalized curvilinear coordinates

Hejranfar, K ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1103/PhysRevE.95.023314
  3. Abstract:
  4. In this work, a high-order weighted essentially nonoscillatory (WENO) finite-difference lattice Boltzmann method (WENOLBM) is developed and assessed for an accurate simulation of incompressible flows. To handle curved geometries with nonuniform grids, the incompressible form of the discrete Boltzmann equation with the Bhatnagar-Gross-Krook (BGK) approximation is transformed into the generalized curvilinear coordinates and the spatial derivatives of the resulting lattice Boltzmann equation in the computational plane are solved using the fifth-order WENO scheme. The first-order implicit-explicit Runge-Kutta scheme and also the fourth-order Runge-Kutta explicit time integrating scheme are adopted for the discretization of the temporal term. To examine the accuracy and performance of the present solution procedure based on the WENOLBM developed, different benchmark test cases are simulated as follows: unsteady Taylor-Green vortex, unsteady doubly periodic shear layer flow, steady flow in a two-dimensional (2D) cavity, steady cylindrical Couette flow, steady flow over a 2D circular cylinder, and steady and unsteady flows over a NACA0012 hydrofoil at different flow conditions. Results of the present solution are compared with the existing numerical and experimental results which show good agreement. To show the efficiency and accuracy of the solution methodology, the results are also compared with the developed second-order central-difference finite-volume lattice Boltzmann method and the compact finite-difference lattice Boltzmann method. It is shown that the present numerical scheme is robust, efficient, and accurate for solving steady and unsteady incompressible flows even at high Reynolds number flows. © 2017 American Physical Society
  5. Keywords:
  6. Benchmarking ; Channel flow ; Circular cylinders ; Computational fluid dynamics ; Incompressible flow ; Kinetic theory ; Reynolds number ; Runge Kutta methods ; Shear flow ; Steady flow ; Bhatnagar-gross-krook approximations ; Discrete boltzmann equations ; Finite difference lattice boltzmann method ; Generalized curvilinear coordinates ; High reynolds number flows ; Implicit-explicit runge-kutta schemes ; Lattice boltzmann equations ; Weighted essentially nonoscillatory ; Boltzmann equation
  7. Source: Physical Review E ; Volume 95, Issue 2 , 2017 ; 24700045 (ISSN)
  8. URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.023314