NERSC 1999 Annual Report

George Vahala, College of William and Mary
Pavol Pavlo, Institute of Plasma Physics,
Czech Academy of Sciences, Prague
Linda Vahala, Old Dominion University

Research Objectives

Novel thermal lattice Boltzmann simulations (TLBM) are being investigated to consider parameter regimes appropriate for the tokamak divertor. TLBM are much better suited for MPP systems than computational fluid dynamics (CFD) codes. In the divertor region there are time varying regimes in which the neutral collisionality ranges from highly collisional (well treated by fluid equations) to weakly collisional (requiring Monte Carlo). It is numerically stiff to couple fluid and kinetic codes due to the disparate spatial and temporal scales. However, this stiffness is avoided when coupling TLBM to Monte Carlo, since both these descriptions are kinetic.

Computational Approach

TLBM codes solve the linearized Bhatnagar-Gross-Krook (BGK) system and so involve: (a) computation of the mean density, velocity, and temperature at each spatial node; (b) collisional relaxation; and (c) Lagrangian free-streaming. Our TLBM code has two computational kernels which act only on local data, and a streaming operation that passes boundary data between PEs.

Accomplishments


	Propagation of a 2D jet into a strongly stratified gas.

The simplicity of TLBM has a drawback-numerical instability. As more and more moment constraints are imposed on the distribution function, the further one must go in Taylor expansions in the mean velocity for the relaxed distribution function. To eliminate discrete lattice symmetry effects that can enter into the higher moment equations, the relaxed distribution function must not be a Maxwellian. Hence there is no H-theorem for TLBM. We have been exploring the utilization of higher isotropy phase space velocity lattices-in particular, the octagonal lattice in 2D (with its 53-bit generalization to 3D). This forces us to decouple the velocity lattice from the spatial grid, since an octagonal lattice is not space-filling. The use of second-order interpolation does not introduce measurable numerical viscosity or conductivity. These higher isotropy lattices are much more numerically stable. Further generalizations are being considered in allowing the streaming to be nodal temperature dependent. This allows simulations of flows with Mach numbers up to 0.5.

We have also extended our TLBM to multiple species in preparation for plasma divertor studies. This multi-species model will be used to solve models like the UEDGE-Navier-Stokes coupled set of equations. For 2D turbulence, we have investigated the interaction and relaxation of double vortex layers that are perpendicular to each other.

Significance

In the standard CFD approach to solving the nonlinear equations, one must handle the nonlinear Riemann problem, which consumes over 30% of the CPU time in accurate resolution of the nonlinear convective derivative. In TLBM, one sidesteps the Riemann problem altogether and can use Lagrangian streaming to handle the (linear) advective derivative. By embedding the nonlinear system into higher dimensional phase space (i.e., by going to a linearized kinetic description), we can choose a simplified system (e.g., a BGK collision operator) to recover the desired equations.

Publications

P. Pavlo, G. Vahala, and L. Vahala, "Higher order isotropic velocity grids in lattice methods," Phys. Rev. Lett. 80, 3960 (1998).

G. Vahala, J. Carter, D. Wah, L. Vahala, and P. Pavlo, "Paralleliza-tion and MPI performance of thermal lattice Boltzmann codes for fluid turbulence," in Proc. of the Parallel Computational Fluid Dynamics '99 Conference, edited by Ecer and Emerson (Elsevier Science RV, 1999).

G. Vahala, P. Pavlo, L. Vahala, and N. Martys, "Thermal lattice Boltzmann models for compressible flows," Intern. J. Modern Phys. C9, 1274 (1998).


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