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A dynamically adaptive lattice Boltzmann method for thermal convection problems

100%

Feldhusen K. , Deiterding R. , Wagner C.

International Journal of Applied Mathematics and Computer Science

2016

tom 26

nr 4

735-747

Utilizing the Boussinesq approximation, a double-population incompressible thermal lattice Boltzmann method (LBM) for forced and natural convection in two and three space dimensions is developed and validated. A block-structured dynamic adaptive mesh refinement (AMR) procedure tailored for the LBM is applied to enable computationally efficient simulations of moderate to high Rayleigh number flows which are characterized by a large scale disparity in boundary layers and free stream flow. As test cases, the analytically accessible problem of a two-dimensional (2D) forced convection flow through two porous plates and the non-Cartesian configuration of a heated rotating cylinder are considered. The objective of the latter is to advance the boundary conditions for an accurate treatment of curved boundaries and to demonstrate the effect on the solution. The effectiveness of the overall approach is demonstrated for the natural convection benchmark of a 2D cavity with differentially heated walls at Rayleigh numbers from 103 up to 108. To demonstrate the benefit of the employed AMR procedure for three-dimensional (3D) problems, results from the natural convection in a cubic cavity at Rayleigh numbers from 103 up to 105 are compared with benchmark results.

Thermal and mass diffusion on hydromagnetic flow from a vertical surface with induced magnetic field

88%

Sharma B. K. , Singh S. , Chaudhary R. C.

2007

tom Vol. 12, no 4

1135-1146

The viscous incompressible electrically conducting fluid past an infinite porous vertical plate under the combined buoyancy effects of thermal and mass diffusion has been studied under the action of transverse applied magnetic field taking into account the induced magnetic field, when the plate is subjected to constant heat and mass fluxes (CHFlCMF). The analytical solutions are found for velocity field, temperature distribution, induced magnetic field, current density, concentration field and the expressions for shear stress and rate of heat transfer are obtained and discussed in detail with the help of figures.

A contravariant velocity based implicit multilevel method for simulating the whole process of incompressible flow transition arround Joukowsky airfoils

75%

Liu Z. , Liu C. , Xiong G.

1998

tom Vol. 3, no 1

111-161

A contravanant velocity based incompressible Navier-Stokes governing system is derived to generate an implicit multi-level method so that we can simulate the receptivity and flow transition in cases with complex geometnes. The two- and three- dimensional development of leading-edge receptivity and flow transition in a 2-D Joukowsky airfoil boundary layer are investigated by direct numencal simulation (DNS) using this system. The numencal investigation is based on the so-called spatial approach. The numencal results agree very well with linear stability theory (LST) and the experimental results for the flat plate case. They also agree well with the result obtained by other researchers for the 2-D elliptic leadingedge receptivity case. Some new phenomena for the transition around Joukowsky airfoils are abserved. The details of this approach are described.