Ph.D Thesis

Ph.D StudentWasserman Mark
SubjectMultigrid Acceleration of Turbulent Reacting Flow
DepartmentDepartment of Aerospace Engineering
Supervisors PROFESSOR EMERITUS Jerrold Greenberg
DR. Yair Moryossef
Full Thesis textFull thesis text - English Version


The study at hand is motivated by the ever growing complexity of turbulent combustion CFD simulations, imposing severe demands on computational resources.

As standard numerical methods are inefficient in solving the highly stiff, reacting Reynolds-averaged Navier-Stokes (RANS) equations that govern turbulent combustion, there is a need for methods that accelerate the iterative convergence to a steady-state.

This work investigates the applicability of the multigrid (MG) approach as a means to accelerate convergence by alleviating the inherent numerical stiffness present in the RANS equations, especially when coupled with turbulence and finite-rate chemical kinetics models. A survey of previous attempts at implementing multigrid for the problems at hand indicated extensive use of artificial stabilization to overcome numerical instability arising from non-linearity of source-terms, small-scale physics of combustion, and loss of positivity. To maximize the acceleration offered by multigrid, this work is aimed at developing a robust and stable multigrid method and an implicit solver for turbulent combustion, that do not rely on extensive artificial stabilization.

To tackle the degraded performance of multigrid methods for chemically reacting flows, two major modifications are introduced with respect to the basic Full Approximation Storage (FAS) multigrid method. First, a novel prolongation operator that is based on logarithmic variables is proposed. The new operator prevents loss of positivity due to coarse-grid corrections. The use of a positivity-preserving prolongation operator, together with an extended, unconditionally positive-convergent (UPC) time integration implicit scheme, guarantee unconditional positivity of turbulence quantities and species mass fractions throughout the multigrid simulation. Second, to improve the coarse-grid-correction, a modified defect correction procedure is devised, and successfully applied for the first time to solve turbulent, combusting flows.

The proposed modifications to the standard multigrid algorithm create a well-rounded and robust numerical method that provides accelerated convergence, while unconditionally preserving the positivity of model equation variables. The resulting MG method is suitable for robust simulations of a wide range of flows thanks to being nearly free of artificial stabilization techniques.

Numerical simulations of various turbulent and reacting flows demonstrate that the proposed MG method increases the efficiency by a factor of up to eight (8!) times with respect to an equivalent single-grid method, and by two times with respect to an artificially-stabilized MG method. Moreover, the method has proven to be more stable than an equivalent SG-based method, allowing the use of higher CFL numbers and rapid convergence in cases where the SG-based method failed to converge.