The Barenblatt Turbulent Burst Problem in Kull

Ulitsky, M

Lawrence Livermore National Laboratory

关键词: Partial Differential Equations;    Diffusion;    Computers;    Boundary Conditions;    Buffers;   

DOI  :  10.2172/15016698
RP-ID  :  UCRL-TR-212637
RP-ID  :  W-7405-ENG-48
RP-ID  :  15016698

美国|英语

来源: UNT Digital Library

【 摘 要 】

Significant changes have recently been made to the way in which explicit diffusion is carried out for the turbulent mix model in Kull. That is, the upwind method of calculating divergences of drift/diffusion velocities has been replaced by a more standard treatment, where diffusion coefficients are averaged to the nodes, multiplied by the gradient of some field, and then the usual divergence of this product is taken. Boundary conditions are handled very differently in these two approaches, and for Rayleigh-Taylor problems, the upwind method leads to non-monotonic density profiles and an incorrect treatment of fluxes at mesh boundaries. The more standard approach to diffusion is also taking advantage of the new, more powerful region definition in Kull which puts buffer zones around the region at material boundaries (external zones) and also at mesh boundaries (external surface zones). This allows for much more control of the fluxes at these boundaries, and also saves considerable computer time and memory, since we can now take gradients and divergences of region based fields (rather than the old approach of creating a mesh based field to store the region quantity, performing the differential operators on the mesh based field, and finally storing the mesh based field back in the region variable). To verify that the new diffusion algorithm is working as anticipated, we have selected a nonlinear diffusion-dissipation problem known as the Barenblatt turbulent burst problem. This problem involves solving two coupled nonlinear partial differential equations (a very simplified k-{var_epsilon} model) for the temporal and spatial evolution of the turbulent kinetic energy (k) and the turbulent dissipation rate ({var_epsilon}). What makes this nontrivial problem useful from a verification standpoint is that it has an analytic self-similar solution.