A method for economizing the temporal integration of non-Markovian covariance evolution equations typically arising from renormalized perturbation expansions for classical fields is proposed, based on rational Pade approximations for the time-lagged functions, combined with Gaussian quadrature applied to a coarse-time evolution equation for equal-time covariances. The recursive relations resulting from successive differentiation of the slow-varying form of the dynamic equations for time-lagged functions are used to generate the power series coefficients for the Pade approximants. The method is illustrated by application to the direct interaction approximation for turbulent fluid systems. Computational efficiency comparable to that of Markovian closures is obtained without introduction of arbitrary constants or ad hoc Markovianization assumptions.
Journal of Scientific Computing
- Pub Date:
- Computational Fluid Dynamics;
- Turbulent Flow;
- Pade Approximation;
- Perturbation Theory;
- Fluid Mechanics and Heat Transfer