Narrow Results

In this paper, the computational examination is carried out on the heat generation, Soret and Dufour’s influence on the unsteady MHD convection flow of an incompressible viscous fluid with chemical reaction. It is due to the exponentially accelerated vertical porous plate embedded in a permeable medium with ramped wall temperature together with surface concentration and also with thermal radiation impacts. The basic governing set of the equations of the fluid dynamics to the flow is converted into nondimensional form by inserting suitable nondimensional parameters and variables. In addition, the resultant equations are solved computationally with the efficient Crank–Nicolsons implicit finite difference methodology. The influences for several imperative substantial parameters for the model on the velocity, temperature and concentration for the fluids, the skin friction coefficient, Nusselt and Sherwood number for together thermal situations have been explored with the help of graphical profiles and tabular forms. It is found that, the increasing quantities of the Dufour, temperature generation and thermal radiation parameters, the fluid temperature as well as velocity enhances. Similarly, it is noted that an escalating Soret parameter causes the fluid’s velocity and concentration whereas the chemical reaction parameter notifies reversal outputs.

We derive a new relaxation method for the compressible Navier–Stokes equations endowed with general pressure and temperature laws compatible with the existence of an entropy functional and Gibbs relations. Our method is an extension of the energy relaxation method introduced by Coquel and Perthame for the Euler equations. We first introduce a consistent splitting of the diffusion fluxes as well as a global temperature for the relaxation system. We then prove that under the same subcharacteristic conditions as for the relaxed Euler equations and for a specific form of the global temperature and the heat flux splitting, the stability of the relaxation system may be obtained from the non-negativity of a suitable entropy production. A first-order asymptotic analysis around equilibrium states confirms the stability result. Finally, we present a numerical implementation of the method allowing for a straightforward use of Navier–Stokes solvers designed for ideal gases as well as numerical results illustrating the accuracy of the proposed algorithm.

In this paper we will study the condition for the occurrence of flux spikes, such as momentum spikes for the Navier–Stokes equations. Flux spikes are observed in Computational Fluid Dynamics, but it is unknown what are the exact conditions at which they occur and whether they are physical or purely numerical. In the present paper we try to clarify these questions.

A structured overset grid approach coupled with Reynolds-Averaged Navier-Stokes (overset-RANS) method is presented to provide an accurate resolution of two surface ships moving with opposite velocity in viscous fluids. The RANS equations with shear stress transport (SST) k - ω model are employed to treat the viscous turbulent flows. The fully nonlinear boundary condition at the free surface is satisfied at each time step and the evolution of the free surface is achieved by using the level set method. A structured overset grid approach is used to allow flexibility in grid generation, local mesh refinement, as well as the simulation of moving objects while maintaining good grid quality. The presented overset-RANS method is demonstrated by two surface Wigley ship hulls moving with opposite velocity in still water. The simulating results illustrate the feasibility of the presented method to compute the complex viscous free surface flows interacting with many moving ships in still water or in waves.

We study the properties of vacuum states in weak solutions to the compressible Navier–Stokes system with spherical symmetry. It is shown that vacuum states cannot develop later on in time in a region far away from the center of symmetry, provided there is no vacuum state initially and two initially non-interacting vacuum regions never meet each other in the future. Furthermore, a sufficient condition on the regularity of the velocity excluding the formation of vacuum states is given.

An anisotropic Cartesian grid (ACG) method is developed for viscous flow computations. This method is more compatible with the anisotropic feature of flows near the body than the traditional isotropic Cartesian grid (ICG) method and is therefore grid saving. An efficient algorithm for ACG generation is presented and analyzed. A bilinear interpolation is applied to construct an easily implementable second-order accurate solid wall condition. The stability of this solid wall treatment is established using the GKS-stability theory. The ACG method along with the solid wall condition is finally validated by computing viscous flows around airfoils. The ACG method is compared with the ICG method. It is found that the ACG method can significantly save the number of grid points without jeopadizing the accuracy. Such a gain can be expected to be substantially more important in three-dimensional flow computations.