Gopal Patnaik

A barely implicit correction for flux-corrected transport

Abstract The barely implicit correction (BIC) removes the stringent limit on the timestep imposed; by the sound speed in explicit methods. This is done by adding one elliptic equation which has to be solved implicitly. BIC is combined with the flux-corrected transport algorithm in order to represent sharp gradients in subsonic flows accurately. The resultant conservative algorithm costs about the same per timestep as a single explicit timestep calculated using an optimized FCT module. Several examples show the techniques ability to solve nearly incompressible flows very economically.

Detailed numerical simulations of cellular flames

Time-dependent, two-dimensional simulations of perturbed premixed laminar flames have been used to study the development of cellular structures in rich and lean hydrogen flames. The model includes detailed hydrogen-oxygen combustion with 24 elementary reactions of eight reactive species and a nitrogen diluent, molecular diffusion of all species, thermal conduction, and convection. Calculations of perturbed lean hydrogen flame evolution showed that the flame was unstable at the front, and the structure that evolved resembled cellular structures observed in experiments. The same perturbation applied to a rich hydrogen flame showed that the perturbation died out and cellular structures did not appear. Binary diffusion coefficients were varied to test the role of molecular diffusion in the development of cellular structure. When the coefficient of molecular hydrogen was set equal to that of molecular oxygen, the perturbation died out; when the coefficient of molecular oxygen was set equal to that of molecular hydrogen, the instability persisted. The results of the simulations support the diffusional-thermal theory of flame instability.

Effect of gravity on flame instabilities in premixed gases

The effects of gravity on instabilities in laminar, premixed flames in dilute H 2 -O 2 -N 2 mixtures is investigated using detailed, time-dependent, two-dimensional numerical simulations. The physical processes included in the model are fluid convection, detailed hydrogen-oxygen chemistry, multispecies diffusion, thermal conduction, viscosity, and gravity. The results from the simulations show that the effects of gravity become more important as the burning velocity of a mixture is decreased by either decreasing the amount of fuel or increasing the amount of diluent

Quantifying residual numerical diffusion in flux-corrected transport algorithms

Residual diffusion in fluid-dynamics calculations results from the finite order of approximation in the underlying linear algorithm, including the effect of smoothing sometimes added for numerical reasons, and, in the case of monotonicity-preserving algorithms such as flux-corrected transport (FCT), the nonlinear action of the flux limiter on steep profiles. Some widely used FCT algorithms contain a multiplicative constant that reduces the antidiffusion coefficient by ∼0.01%–0.1%. Replacing this constant with a smoothly varying function of velocity which equals unity when the Courant number vanishes causes the linear diffusion to go to zero when the flow velocity does. The use of a velocity-dependent antidiffusion coefficient minimizes numerical smearing of discontinuities and associated effects in the neighboring flow. Computational examples are presented. The residual diffusion for nonzero flow speeds is nonlinear and problem dependent. A method is presented for calibrating it in any given code in the context of a particular problem, and is applied to the FCT algorithms described here.

Load balancing and performance issues for data parallel simulation of stiff chemical nonequilibrium flows

A data parallel program is presented that solves the reactive Euler equations for stiff chemical nonequilibrium flows on Connection Machines CM-2/200 and CM-5/5E. The program is written in CM Fortran and uses direction and time-step splitting to couple representations of the chemical and fluid dynamic processes on a structured Cartesian grid. An explicit high-order monotone algorithm with nonlinear damping is used to integrate the convection terms, and a hybrid asymptotic/modified-Euler approach is used to solve the system of ordinary differential equations from the chemical source terms. Integration of the fluid dynamics was conservatively determined to be 9.4 and 12.0 Gflops on a 512-node CM-5 and CM-5E, respectively. The fluid dynamics solver scaled well for large problems. Therefore, a new load-balancing algorithm was developed that reduces the chemistry integration time by a factor of six for the test problem, a detonation propagating in a hydrogen-oxygen-argon mixture. Moreover, the chemistry integration time, with the load balancing, is slightly less than the time required to integrate the fluid dynamics.

Flow visualization as a basic tool to investigate the dynamics and topology of jets

Issues and difficulties involved in the practical implementation of flow visualization techniques based on a database generated in numerical simulations of unsteady square jets are addressed. Instantaneous visualizations provide basic information on the topological features of the flow, while animation of these visualizations gives an insight into the detailed dynamics of formation, development, and interaction of the coherent structures controlling the entrainment and mixing processes.<<ETX>>

Load Balancing and Performance Issues for Data Parallel

A data parallel program is presented that solves the reactive Euler equations for stiff chemical nonequilibrium ows on Connection Machines CM-2/200 and CM-5/5E. The program is written in CM Fortran and uses direction and time-step splitting to couple representations of the chemical and uid dynamicprocesses on a structured Cartesian grid.An explicit high-ordermonotonealgorithmwith nonlineardamping is used to integrate the convection terms, and a hybrid asymptotic/modi® ed-Euler approach is used to solve the system of ordinary differential equations from the chemical source terms. Integration of the uid dynamics was conservatively determined to be 9.4 and 12.0 G ops on a 512-node CM-5 and CM-5E, respectively. The uid dynamics solver scaled well for large problems; however, both the performance and the scaling are signi® cantly affected by the nearest-neighbor communications, which accounted for at least 24% of the execution time on the CM-5. For the integration of the chemistry source terms, poor load balancing signi® cantly affected performance of the program. Therefore, a new load-balancing algorithmwas developed that reduces the chemistry integration time by a factor of six for the test problem, a detonation propagating in a hydrogen± oxygen± argon mixture. Moreover, the chemistry integration time, with the load balancing, is slightly less than the time required to integrate the uid dynamics. As a result, an ef® cient data parallel program for solving stiff chemical nonequilibrium ows is available for problems that were too expensive to solve in the past.

Load balancing and performance issues for the data parallel simulation of stiff chemical nonequilibrium flows

A data parallel program is presented that solves the reactive Euler equations for stiff chemical nonequilibrium flows on Connection Machines CM-2/200 and CM-5/5E. The program is written in CM Fortran and uses direction and time-step splitting to couple representations of the chemical and fluid dynamic processes on a structured Cartesian grid. An explicit high-order monotone algorithm with nonlinear damping is used to integrate the convection terms, and a hybrid asymptotic/modified-Euler approach is used to solve the system of ordinary differential equations from the chemical source terms. Integration of the fluid dynamics was conservatively determined to be 9.4 and 12.0 Gflops on a 512-node CM-5 and CM-5E, respectively. The fluid dynamics solver scaled well for large problems. Therefore, a new load-balancing algorithm was developed that reduces the chemistry integration time by a factor of six for the test problem, a detonation propagating in a hydrogen-oxygen-argon mixture. Moreover, the chemistry integration time, with the load balancing, is slightly less than the time required to integrate the fluid dynamics.