|Ph.D Student||Moryossef Yair|
|Subject||Unconditionally Positive Implicit Method for Two-Equation|
|Department||Department of Aerospace Engineering||Supervisors||Professor Dan Givoli|
|Dr. Yuval Levy|
|Full Thesis text|
Among the various turbulence modeling techniques, two-equation turbulence models are probably the most widely used in the field of computational fluid dynamics. The required numerical treatment of two-equation turbulence models is far from trivial as it presents serious difficulties. Among these are, poor convergence behavior and loss of the physics based positivity characteristics of the turbulence quantities. The success of turbulent flow simulations relies heavily on the numerical stability of the numerical method applied to the turbulence models. The motivation of the current work is to develop a general framework for positivity preservation and for guaranteeing convergence for two-equation turbulence models.
A new general implicit procedure that guarantees the positivity of turbulence model equations dependent variables is developed. The implicit procedure is based on designing the implicit Jacobian to be an M-matrix. A unified approach for the treatment of the convection, diffusion, and source terms is introduced and employed. An appropriate design of the M-matrix guarantees the positivity of the turbulence equation dependent variables for any time step, without the use of any clipping.
The procedure is employed and demonstrated using a two-equation linear k-ω turbulence model and a non-linear k-ε turbulence model. An efficient construction of the Jacobian matrix is introduced, resulting in diagonal matrices. The models are tested by simulating steady and unsteady complex flow fields. Results from the numerical simulations show that the new procedure exhibits very good convergence characteristics, is extremely robust, and most importantly, it always preserves the positivity of the turbulence variables.