Implementation of Dynamic Density Functional Theory for Self-Organizing Complex Fluids on Parallel Computers

摘要

In this paper we elaborate on a new method for the calculation of diffusional relaxation mechanisms in complex self-organizing fluids on a mesoscopic level. The applications are in the development and design of industrial polymer and surfactant materials, and also in the understanding of active biological fluids for biotechnology applications. The method entails repeated inversion of a highly non-linear density functional transform. The problem is gargantuan: O(10~4 - 10~6) nonlinear equations have to be solved each of the O(10~5 - 10~6) time steps. However, simulations of practical interest can be done, using the parallel computer CM5. The data-parallel language CM Fortran is well suited for rapid implementation of the numerical algorithms. Conversion of the CM Fortran code to more general F90 (IBM) is demonstrated. The foremost technical bottlenecks are the efficient implementations of (ⅰ) a generalised fully symmetric finite difference operator, (ⅱ) the implementation of an efficient multi-component random isotropic flux generator and (ⅲ) the implementation of a preconditioner for solving the non-linear equations.