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This paper investigates a high performance implementation of an Arbitrary Lagrangian Eulerian moving mesh technique on shared memory systems using OpenMP environment. Moving mesh techniques are considered an integral part of a wider class of fluid mechanics problems that involve moving and deforming spatial domains, namely, free-surface flows and Fluid Structure Interaction (FSI). The moving mesh technique adopted in this work is based on the notion of nodes relocation, subjected to a certain evolution as well as constraint conditions. A conjugate gradient method augmented with preconditioning is employed for solution of the resulting system of equations. The proposed algorithm, initially, reorders the mesh using an efficient divide and conquer approach and then parallelizes the ALE moving mesh scheme. Numerical simulations are conducted on the multicore AMD Opteron and Intel Xeon processors, and unstructured triangular and tetrahedral meshes are used for the 2D and 3D problems. The quality of generated meshes is checked by comparing the element Jacobians in the reference and current meshes, and by keeping track of the change in the interior angles in triangles and tetrahedrons. Overall, 51 and 72% efficiencies in terms of speedup are achieved for both the parallel mesh reordering and ALE moving mesh algorithms, respectively.

The generalized magnetohydrodynamics (MHD) free convection flow of a Casson fluid through a channel immersed in a porous media with mass and heat transfer is considered. With heat generation, the contribution of concentration gradient is taken into account for heat flux (Dufour effect), and chemical reaction of order first for species balance is also considered. Initially, governing equations of flow model are reduced to nondimensional equations and then solved analytically. The transformed solutions for concentration, temperature, and velocity are written in summation form to invert by Laplace transform easily. The closed form solution of field variables has been plotted graphically due to different parametric variations to analyze the behavior of concentration, temperature, and flow fields against the physical parameters. Furthermore, comparisons among fractionalized and ordinary concentration, temperature, and velocity fields are made to see the effect of parameter 𝛼. It is concluded that concentration, temperature, and velocity obtained with fractional derivative are smaller than that obtained by ordinary derivative. Therefore, fractional derivative is the best choice to obtain controlled concentration, temperature, and velocity.

Unsteady magnetohydrodynamics (MHD) flow of fractionalized Brinkman-type fluid over a vertical plate is discussed. In the model of problem, additional effects such as heat generation/absorption and chemical reaction are also considered. The model is solved by using the Caputo fractional derivative. The governing dimensionless equations for velocity, concentration, and temperature profiles are solved using the Laplace transform method and compared graphically. The effects of different parameters like fractional parameter, heat generation/absorption Q , chemical reaction R, and magnetic parameter M are discussed through numerous graphs. Furthermore, comparison among ordinary and fractionalized velocity fields are also drawn. From the figures, it is observed that chemical reaction and magnetic field have decreasing effect on velocity profile, whereas thermal radiation and mass Grashof numbers have increasing effect on the velocity of the fluid.

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