Ricerc@Sapienza

Many physical multiscale problems are characterized by phenomena having wide ranges of spatial and temporal scales. When a system of partial differential equations is employed to model such phenomena, high resolution discretization is required for solving the finest spatial scales, such as steep gradients, singularities or near singularities. These problems are generally impractical to solve on a fixed computational grid, and require enormous computational resources in terms of memory storage and computing time. The aim of this project is to adopt an existing in-house adaptive numerical multiresolution algorithm based on the wavelet transform for the generation of flamelet-based thermodynamic database, which will be of aid for the numerical simulation of multidimensional reactive flows characterizing high pressure combustion devices. This wavelet-based discretization method allows to obtain spatial grid adaption, simply removing grid points associated to small bases functions amplitudes, reducing the number of degrees of freedom and obtaining, at the same time, accurate solutions matched to the scales of the physical problem.
A further opportunity to reduce the complexity of the problem, with corresponding saving in computational work, is represented by the G-Scheme, an existing in-house algorithm useful to achieve multi-scale adaptive model reduction along-with the integration of the differential equations. It assumes that the problem dynamics can be decomposed into active, slow, fast, and invariant subspaces. The algorithm allows to integrate only the degrees of freedom belonging to the active dynamics, choosing a time step of the same order of magnitude of the fastest time scale belonging to the active subspace.