Engineering topics
Publications and source records attributed to Djomehri, M. J..
CFD applications require high-performance computational platforms: 1. Complex physics and domain configuration demand strongly coupled solutions; 2. Applications are CPU and memory intensive; and 3. Huge resource requirements can only be satisfied by teraflop-scale machines or distributed computing.
A rigorous stability estimate for arbitrary order of accuracy of spatial central difference schemes for initial-boundary value problems of nonlinear symmetrizable systems of hyperbolic conservation laws was established recently by Olsson and Oliger (1994) and Olsson (1995) and was applied to the two-dimensional compressible Euler equations for a perfect gas by Gerritsen and Olsson (1996) and Gerritsen (1996). The basic building block in developing the stability estimate is a generalized energy approach based on a special splitting of the flux derivative via a convex entropy function and certain homogeneous properties. Due to some of the unique properties of the compressible Euler equations for a perfect gas, the splitting resulted in the sum of a conservative portion and a non-conservative portion of the flux derivative. hereafter referred to as the "Entropy Splitting." There are several potential desirable attributes and side benefits of the entropy splitting for the compressible Euler equations that were not fully explored in Gerritsen and Olsson. The paper has several objectives. The first is to investigate the choice of the arbitrary parameter that determines the amount of splitting and its dependence on the type of physics of current interest to computational fluid dynamics. The second is to investigate in what manner the splitting affects the nonlinear stability of the central schemes for long time integrations of unsteady flows such as in nonlinear aeroacoustics and turbulence dynamics. If numerical dissipation indeed is needed to stabilize the central scheme, can the splitting help minimize the numerical dissipation compared to its un-split cousin? Extensive numerical study on the vortex preservation capability of the splitting in conjunction with central schemes for long time integrations will be presented. The third is to study the effect of the non-conservative proportion of splitting in obtaining the correct shock location for high speed complex shock-turbulence interactions. The fourth is to determine if this method can be extended to other physical equations of state and other evolutionary equation sets. If numerical dissipation is needed, the Yee, Sandham, and Djomehri (1999) numerical dissipation is employed. The Yee et al. schemes fit in the Olsson and Oliger framework.
An approach which closely maintains the non-dissipative nature of classical fourth or higher- order spatial differencing away from shock waves and steep gradient regions while being capable of accurately capturing discontinuities, steep gradient and fine scale turbulent structures in a stable and efficient manner is described. The approach is a generalization of the method of Gustafsson and Olsson and the artificial compression method (ACM) of Harten. Spatially non-dissipative fourth or higher-order compact and non-compact spatial differencings are used as the base schemes. Instead of applying a scalar filter as in Gustafsson and Olsson, an ACM like term is used to signal the appropriate amount of second or third-order TVD or ENO types of characteristic based numerical dissipation. This term acts as a characteristic filter to minimize numerical dissipation for the overall scheme. For time-accurate computations, time discretizations with low dissipation are used. Numerical experiments on 2-D vortical flows, vortex-shock interactions and compressible spatially and temporally evolving mixing layers showed that the proposed schemes have the desired property with only a 10% increase in operations count over standard second-order TVD schemes. Aside from the ability to accurately capture shock-turbulence interaction flows, this approach is also capable of accurately preserving vortex convection. Higher accuracy is achieved with fewer grid points when compared to that of standard second-order TVD or ENO schemes. To demonstrate the applicability of these schemes in sustaining turbulence where shock waves are absent, a simulation of 3-D compressible turbulent channel flow in a small domain is conducted.
An approach which closely maintains the non-dissipative nature of classical fourth or higher- order spatial differencing away from shock waves and steep gradient regions while being capable of accurately capturing discontinuities, steep gradient and fine scale turbulent structures in a stable and efficient manner is described. The approach is a generalization of the method of Gustafsson and Oisson and the artificial compression method (ACM) of Harten. Spatially non-dissipative fourth or higher-order compact and non-compact spatial differencings are used as the base schemes. Instead of applying a scalar filter as in Gustafsson and Olsson, an ACM like term is used to signal the appropriate amount of second or third-order TVD or ENO types of characteristic based numerical dissipation. This term acts as a characteristic filter to minimize numerical dissipation for the overall scheme. For time-accurate computations, time discretizations with low dissipation are used. Numerical experiments on 2-D vortical flows, vortex-shock interactions and compressible spatially and temporally evolving mixing layers showed that the proposed schemes have the desired property with only a 10% increase in operations count over standard second-order TVD schemes. Aside from the ability to accurately capture shock-turbulence interaction flows, this approach is also capable of accurately preserving vortex convection. Higher accuracy is achieved with fewer grid points when compared to that of standard second-order TVD or ENO schemes. To demonstrate the applicability of these schemes in sustaining turbulence where shock waves are absent, a simulation of 3-D compressible turbulent channel flow in a small domain is conducted.
We present a methodology for the numerical simulation of flow fields by the simultaneous application of two distinct approaches to computational aerodynamics. We compute the three dimensional flow field of a missile at moderate angle of attack by dividing the flow field into two regions: a region near the surface where we use a structured grid and a Navier Stokes solver, and a region farther away from the surface where we utilize an unstructured grid and an Euler solver. The two solvers execute as independent UNIX processes either on the same machine or on two machines. The solvers communicate data across their common interfaces within the same machine or over the network. The computations indicate that extensively separated flow fields can be computed without significant distortion by combining viscous and inviscid solvers.
Applicability of a three-dimensional solution adaptive unstructured tetrahedral Euler flow solver about generic models for near-field sonic boom pressure signature predictions is evaluated. Comparisons of computational and experimental data demonstrates the capability of the method for predicting inviscid solutions useful for high speed calculations about simple 3-D geometries. The approach has promising features and results indicate potential for application to more complex configurations. The mesh generation is based on the advancing front technique, and steady state solutions of the Euler equations are achieved by explicit time integration. Spatial discretization uses the Taylor-Galerkin approach; an alternate time integration, based on the Runge-Kutta method, is also included. The solution-adaptive grid procedure is based on either remeshing or mesh refinement techniques. An alternative geometry-adaptive grid procedure has also been incorporated.
A molecular-dynamics simulation of hundreds of ions confined in a Paul trap has been performed. The simulation includes the trapped particles' micromotion and interparticle Coulomb interactions. A random walk in velocity was implemented to bring the secular motion to a given temperature which was numerically measured. When the coupling Gamma is large the ions from concentric shells which undergo a quadrupole oscillation at the RF frequency, while the ions within a shell form a 2D hexagonal lattice. Ion clouds at 5 mK show no RF heating for q(z) less than about 0.6, whereas rapid heating is seen for qz = 0.8.
A generic solution-adaptive grid program based on an error equi-distribution concept has been developed for use in complex multidimensional flows. The capability of a generic, user-friendly, multidimensional algorithm is demonstrated using several complex 3D flows in high-speed regimes. A simple scheme enforces the continuity of grid spacing along each currently adapted grid line as the computation proceeds. Calculation of normal vectors at each point of a grid plane is enhanced. The grid movement is automatically controlled by reinstating grid-spacing continuity locally in the mainstream of the unidirectional computation. It is concluded that the scheme can be readily coupled with many flow solvers to enhance accuracy and efficiency of solutions.