Development of Algorithms for Nonlinear Physics on Type-II Quantum Computers
Final technical rept. 1 Feb 2004-31 Jan 2007
COLLEGE OF WILLIAM AND MARY WILLIAMSBURG VA
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Using CAP resources we have been able to uncover lattice geometry effects in the entropic lattice Boltzmann algorithm that had not been expected from lower grid resolution runs. In the entropic formulation, one is working with a generalized BGK collision operator that has within it the germs of detailed balance. Thus, the unconditionally stable algorithm is achieved with a variable transport coefficient, not unlike Large Eddy Simulations LES in CFD. Indeed, we have explored this connection in some detail but will report those findings elsewhere due to space limitations here. Another unexpected result unearthed by the CAP runs was the dependence of the ELB on the Mach number. A low Mach number expansion has to be performed to analytically evaluate the Lagrange multipliers arising in the extremization of the H-function subject to local collisional constraints. We have found that the Qi 5-bit model is less sensitive to the flow Mach number than the Q27-bit model. Another somewhat unexpected finding was the importance of maintaining the distribution function correlations in the mesoscopic description. To perform the long-time 1 600 grid runs we needed to perform continuation runs. In the early stages of CAP we tried to minimize the amount of io read-outread-in and to reconstruct the relaxation distribution function from its moments rather than keeping the full correlation information. While this did not affect the energy decay, there were significant discontinuities introduced into the enstrophy and higher energy spectral moments. The parallelization strength of ELB arises from the modeling of the macroscopic nonlinear derivatives by local moments. Chapman-Enskog asymptotics will then, on projecting back into physical space, yield these nonlinear derivatives.
- Numerical Mathematics
- Fluid Mechanics
- Quantum Theory and Relativity