Simulation of turbulent flows using nodal integral method

Nodal methods are the backbone of the production codes for neutron-diffusion and transport equations. Despite their high accuracy, use of these methods for simulation of fluid flow is relatively new. Recently, a modified nodal integral method (MNIM) has been developed for simulation of laminar flows. In view of its high accuracy and efficiency, extension of this method for the simulation of turbulent flows is a logical step forward. In this dissertation, MNIM is extended in two ways to simulate incompressible turbulent flows---a new MNIM is developed for the 2D k-epsilon equations; and 3D, parallel MNIM is developed for direct numerical simulations. Both developments are validated, and test problems are solved.;In this dissertation, a new nodal numerical scheme is developed to solve the k-epsilon equations to simulate turbulent flows. The MNIM developed earlier for laminar flow equations is modified to incorporate eddy viscosity approximation and coupled with the above mentioned schemes for the k and epsilon equations, to complete the implementation of the numerical scheme for the k-epsilon model. The scheme developed is validated by comparing the results obtained by the developed method with the results available in the literature obtained using direct numerical simulations (DNS). The results of current simulations match reasonably well with the DNS results. The discrepancies in the results are mainly due to the limitations of the k-epsilon model rather than the deficiency in the developed MNIM.;A parallel version of the MNIM is needed to enhance its capability, in order to carry out DNS of the turbulent flows. The parallelization of the scheme, however, presents some unique challenges as dependencies of the discrete variables are different from those that exist in other schemes (for example in finite volume based schemes). Hence, a parallel MNIM (PMNIM) is developed and implemented into a computer code with communication strategies based on the above mentioned dependencies. The speedup and efficiency of the PMNIM are analyzed for a laminar flow test problem. The efficiency, calculated based on Gustafson's law, is found to be more than 75% for a 20 x 20 x 20 mesh and remains almost constant as number of processors is increased. It can be concluded that the PMNIM is reliable, scalable and efficient.;The PMNIM is then used to study the transition to turbulence in Arnold-Beltrami-Childress (ABC) flows. These flows display the interesting phenomenon of heteroclinic cycles. The results are obtained for two wavenumbers: k = 1 (also studied earlier by other researchers) and k = 2, respectively. The results for k = 1 are compared with those obtained using the pseudo spectral method. The comparison shows good agreement and also shows that results obtained with similar grid sizes and time steps match very well with those obtained using pseudo spectral method. New results are obtained for k = 2, and the heteroclinic cycles observed in this flow are discussed and contrasted with those obtained in the flow with k = 1. The results show that the flow becomes unstable for the k = 2 case at smaller Reynolds number than that for k = 1. The flow also shows some very interesting phenomena such as simultaneous existence of the two types of heteroclinic cycles.