O presente trabalho estuda em detalhe o modelo parietal transiente de Walker et al. (1989, AIAA J., 27, 140-149) para perfis de velocidade em escoamentos turbulentos. Dois novos termos são adicionados ao sistema transcedental não linear de equações que é utilizado para determinar os três principais parâmetros do modelo. Os domínios matemático e físico de validade do modelo são determinados como uma função do parâmetro gradiente de pressão adimensional (p+). Uma parametrização explícita em termos de p+ é apresentada para o período médio entre eventos (), para a origem do tempo () e para a constante de integração (A0) da equação dependente do tempo. Na presente análise, todos os sistemas de equações diferenciais são transformados, resultando em um procedimento computacional rápido que pode ser utilizado para o desenvolvimento de simuladores em tempo real.

The present work studies, in detail, the unsteady wall-layer model of Walker et al. (1989, AIAA J., 27, 140 – 149) for the velocity profile in turbulent flows. Two new terms are included in the transcendental non-linear system of equations that is used to determine the three main model parameters. The mathematical and physical feasible domains of the model are determined as a function of the non-dimensional pressure gradient parameter (p+). An explicit parameterization is presented for the average period between bursts (), the origin of time () and the integration constant of the time dependent equation (A0) in terms of p+. In the present procedure, all working systems of differential equations are transformed, resulting in a very fast computational procedure that can be used to develop real-time flow simulators.

The Mathematica system (version 4.0) is employed in the solution of nonlinear difusion and convection-difusion problems, formulated as transient one-dimensional partial diferential equations with potential dependent equation coefficients. The Generalized Integral Transform Technique (GITT) is first implemented for the hybrid numerical-analytical solution of such classes of problems, through the symbolic integral transformation and elimination of the space variable, followed by the utilization of the built-in Mathematica function NDSolve for handling the resulting transformed ODE system. This approach ofers an error-controlled final numerical solution, through the simultaneous control of local errors in this reliable ODE's solver and of the proposed eigenfunction expansion truncation order. For covalidation purposes, the same built-in function NDSolve is employed in the direct solution of these partial diferential equations, as made possible by the algorithms implemented in Mathematica (versions 3.0 and up), based on application of the method of lines. Various numerical experiments are performed and relative merits of each approach are critically pointed out.