This article studies the motion of temperature dependent plastic dynamic viscosity and thermal conductivity of steady incompressible laminar free convective magnetohydrodynamic (MHD) Casson fluid flow over an exponentially stretching surface with suction and exponentially decaying internal heat generation. It is assumed that the natural convection is driven by buoyancy and space dependent heat generation. The viscosity and thermal conductivity of Casson fluid is assumed to vary as a linear function of temperature. By using suitable transformation, the governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear coupled ordinary differential equations and solved by the Homotopy analysis method. A new kind of averaged residual error is adopted and used to find the optimal convergence control parameter. A parametric study is performed to illustrate the influence of Prandtl number, Casson parameter, temperature dependent viscosity, temperature dependent thermal conductivity, Magnetic parameter and heat source parameter on the fluid velocity and temperature profiles within the boundary layer. The flow controlling parameters are found to have a profound effect on the resulting flow profiles

The usual concept of simulation methods for turbulent flows is to impose a certain (partial) flow resolution. This concept becomes problematic away from limit regimes of no or an almost complete flow resolution: discrepancies between the imposed and actual flow resolution may imply an unreliable model behavior and high computational cost to compensate for simulation deficiencies. An exact mathematical approach based on variational analysis provides a solution to these problems. Minimal error continuous eddy simulation (CES) designed in this way enables simulations in which the model actively responds to variations in flow resolution by increasing or decreasing its contribution to the simulation as required. This paper presents the first application of CES methods to a moderately complex, relatively high Reynolds number turbulent flow simulation: the NASA wall-mounted hump flow. It is shown that CES performs equally well or better than almost resolving simulation methods at a little fraction of computational cost. Significant computational cost and performance advantages are reported in comparison to popular partially resolving simulation methods including detached eddy simulation and wall-modeled large eddy simulation. Characteristic features of the asymptotic flow structure are identified on the basis of CES simulations.

Reynolds-averaged Navier–Stokes (RANS), large eddy simulation (LES), and hybrid RANS-LES, first of all wall-modeled LES (WMLES) and detached eddy simulation (DES) methods, are regularly applied for wall-bounded turbulent flow simulations. Their characteristic advantages and disadvantages are well known: significant challenges arise from simulation performance, computational cost, and functionality issues. This paper describes the application of a new simulation approach: continuous eddy simulation (CES). CES is based on exact mathematics, and it is a minimal error method. Its functionality is different from currently applied simulation concepts. Knowledge of the actual amount of flow resolution enables the model to properly adjust to simulations by increasing or decreasing its contribution. The flow considered is a high Reynolds number complex flow, the Bachalo–Johnson axisymmetric transonic bump flow, which is often applied to evaluate the performance of turbulence models. A thorough analysis of simulation performance, computational cost, and functionality features of the CES model applied is presented in comparison with corresponding features of RANS, DES, WMLES, and wall-resolved LES (WRLES). We conclude that CES performs better than RANS, DES, WMLES, and even WRLES at a little fraction of computational cost applied for the latter methods. CES is independent of usual functionality requirements of other methods, which offers relevant additional advantages.

The simulation of high Reynolds number (Re) separated turbulent flows faces significant problems for decades: large eddy simulation (LES) is computationally too expensive, and Reynolds-averaged Navier-Stokes (RANS) methods and hybrid RANS-LES methods often provide unreliable results. This has serious consequences, we are currently unable to reliably predict very high Re regimes, which hampers applications and our understanding of turbulence structures. The paper reports the advantages of a strict mathematical approach, continuous eddy simulation (CES), to derive partially resolving turbulence models. In contrast to popular hybrid RANS-LES, this minimal error approach includes a dynamic modification of the turbulence model in response to the actual flow resolution: the model can increase (decrease) its contribution to the simulation in dependence of a low (high) flow resolution. This property is the essential requirement to seamlessly cover RANS and LES regimes. The CES modeling approach offers essential advantages regarding its functionality: basically, it is independent of a variety of simulation settings applied in popular hybrid RANS-LES to improve the model performance. In addition, the CES computational cost can be below the cost of other hybrid RANS-LES and LES by orders of magnitude. Essential simulation performance advantages of CES simulations are described here with respect to three complex flow applications: periodic hill flows at high Reynolds number, the NASA wall-mounted hump flow, and the Bachalo & Johnson axisymmetric transonic bump flow.