Phase-field models have emerged as a successful class of models in a wide variety of applications in computational materials science. Multiphase field theories, as a subclass of phase-field theories, have been especially useful for studying nucleation and growth in polycrystalline materials. In theory, an infinite number of phase-field variables are required to represent grain orientations in a rotationally invariant free energy. However, limitations on available computational time and memory have restricted the number of phase-field variables used in the simulations. We present an approach by which the time and memory requirements are drastically reduced relative to standard algorithms. The proposed algorithm allows us the use of an unlimited number of phase-field variables to perform simulations without the associated burden on computational time or memory. We present the algorithm in the context of coalescence free grain growth.

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SUMMARYA benchmark quality solution is presented for ow in a staggered double lid driven cavity obtained by using the wavelet-based discrete singular convolution (DSC). The proposed wavelet based algorithm combines local methods' exibility and global methods' accuracy, and hence, is a promising approach for achieving the high accuracy solution of the Navier-Stokes equations. Block structured grids with pseudo-overlapping subdomains are employed in the present simulation. A third order RungeKutta scheme is used for the temporal discretization. Quantitative results are presented, apart from the qualitative uid ow patterns. The prevalence of rich features of ow morphology, such as two primary vortex patterns, merged single primary vortex patterns, and secondary eddies, makes this problem very attractive and interesting. The problem is quite challenging for the possible existence of numerically induced asymmetric ow patterns and elliptic instability. Important computational issues like consistence, convergence and reliability of the numerical scheme are examined. The DSC algorithm is tested on the single lid driven cavity ow and the Taylor problem with a closed form solution. The double lid driven cavity simulations are cross-validated with the standard second order ÿnite volume method.

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