In spite of today's progress in Large Eddy Simulation (LES) in simulating wide variety of flows, statistical models are widely used for the simulations of practical flows of the industry. Nevertheless it is necessary to develop, analyze and optimize these models. The present work devotes to the development and analysis of advanced models for RANS. These models can predict the effects of non-equilibrium turbulent flows with heat and scalar transfer satisfactorily. The parts of the model are based on explicit algebraic Reynolds stress (EARSM) and scalar flux (EASFM) modeling. The analysis allows firstly the detailed view of separated physical mechanisms and later it can be useful for simulating complex flows, swirl flows and transient turbulent flows and scalar transport processes. The first part of this work is to analyze these models by simulating academic configurations and compare with experimental data for validation. Nevertheless these simulations consists the computation of separate flow, secondary flow effects, wall flow, investigation of swirl flow and the flow in rotation system. The development part of this work discusses the optimization strategy and deals with advanced explicit algebraic Reynolds stress models for wall turbulence, strong curvature streamline and non-equilibrium effects (dissipation, anisotropy, nonlinear pressure correlation etc.). Another part of this work consist the application of thermodynamically consistence methods. The second part of this work consist the verification of prediction capability of different model combinations and their application to three complex configurations: (a) different swirl flow with passive scalar transport in the combustion chamber, (b) opened swirl flow with hydro dynamical instability and (c) turbulent flow in square U-channel, especially important in turbomachinery and cooling equipment. From the obtained results one can say that: 1. EARSM/EASFM gives good comparative results compared to Reynolds/scalar flux transport equation models with small numerical problems and computation time. It is valid for steady and also for unsteady investigations. 2. The combination of advanced model are useful in understanding the complex phenomena's like strong wall influence, heat transfer effects.