C, coefficient of pressure C, = We present a new fully-implicit algorithm for unsteady incompressible flow calculations for both the Euler and Navier-Stokes equations. The new method couples the artificial compressibility approach with an implicit A-stable discretization of the unsteady terms in order to advance the solution in a time-accurate manner with no stability limitations on the time step. A pseudotransient steady state problem is solved at each time step to provide a direct coupling between the velocity and pressure fields, and to satisfy the divergence-free constraint.T h e present algorithm solves the pseudotransient problem by using the highly efficient multigrid time stepping technique, originally developed by Jameson [I] for compressible flow calculations. Both viscous and inviscid test problems are presented. An inviscid two-dimensional flow over an oscillating cylinder is used to validate the method by comparison with analytic results. T h e mean quantities of the unsteady viscous flow over a circular cylinder for Re 5 200 are computed and found to be in good agreement with the computational and cxperimental data obtained by other authors. Results for the unsteady viscous flow over a NACA0012 airfoil at 20" angle of attack are also presented, and domain truncation and time resolution effects are discussed. IntroductionThe fast and accurate algorithms for solution of steady state Euler and Navier-Stokes equations developed in recent years have produced very efficient tools for analysis of stationary flows in complex aerospace configurations. In particular, the development of a multigrid schemes has greatly enhanced efficiency of both compressible and incompressible algorithms enabling converged solutions of the threedimensional Euler equations to be obtained in 20 to 50 multigrid steps. However, the increase in convergence rate is achieved at the price of a loss of timeaccuracy. At the same time, efficient time-accurate algorithms for unsteady inviscid and viscous flows are of a great practical interest for a wide range of engineering applications, including free surface, aeroelasticity, and wake flow problems.In this paper we develop a novel approach to increase efficiency of time dependent calculations of incompressible flows in the primitive variable formulation. The method is presented and validated for the full non-linear Euler as well as Navier-Stokes equations.One of the major difficulties encountered in the calculation of incompressible flow is the enforcement of the time-independent constraint on the velocity field imposed by the continuity equation. In order to couple the velocity and pressure fields, Chorin's artificial compressibility approach [3] can be employed. The pseudotemporal evolution for pressure renders the system hyperbolic and allows for the application of fast compressible flow algorithms to march toward the steady state. This method has received a lot of attention and has been applied to rotational inviscid flows by Rizzi and Eriksson 141, Dreyer [5] has appl...

We apply a robust and computationally efficient multigrid-driven algorithm for the simulation of time-dependent three-dimensional incompressible bluff body wakes at low Reynolds numbers (Re less than or equal to 350). The computational algorithm combines a generalized time-accurate artificial compressibility approach, a finite-volume discretization in space, and an implicit backward discretization in time. The solution is advanced in time by performing iterative 'pseudo-transient' steady-state calculations at each time step. The key to the algorithm's efficiency is a powerful multigrid scheme that is employed to accelerate the rate of convergence of the pseudo-transient iteration. The computational efficiency is improved even further by the application of residual smoothing and local pseudo time-stepping techniques, and by using a point-implicit discretization of the unsteady terms. The solver is implemented on a multiprocessor IBM SP2 computer by using the MPI Standard, and a high parallel scalability is demonstrated. The low Reynolds number regime (Re less than or equal to 500) encompasses flow transitions to unsteadiness and to three-dimensionality and attracts considerable attention as an important step on the road to turbulence. In this regime, the slow asymptotics of the wake provide a challenging test for numerical methods since long integration times are necessary to resolve the flow evolution toward a limiting cycle. Our method is extended to three dimensions and applied for low Reynolds number flows over a circular cylinder (Re less than or equal to 250) and a circular semi-cylinder (Re = 350). The computational results are found to be in close agreement with the available experimental and computational data.

No abstract

Point estimation of distribution parameters is considered for a three-parameter compound Poisson process. Formulas are derived for moment method estimation, including estimate biases and the covariance matrix. Asymptotic efficiency of the parameter estimates with a series informant is examined. The efficiency of moment method estimation is computed and analyzed for typical parameter values.

No abstract