Engineering topics

Liou, J.

Publications and source records attributed to Liou, J..

13 records

NASA NTRS1992

Unsteady incompressible flow computations with the finite-element method

While the methods thus far developed for vorticity-streamfunction formulation are thus far restricted to 2D flows, they are applicable to both viscous and inviscid flows, including problems with multiply-connected domains. The present solution techniques for the velocity-pressure formulation can be extended to 3D problems. Attention is given to (1) two multistep formulations that use piecewise bilinear functions for the velocity and piecewise constant functions for the pressure, and (2) a novel multistep velocity-pressure formulation based on the equal-order interpolation of velocity and pressure.

Tezduyar, T. E.↗

NASA NTRS1991

Vorticity-streamfunction formulation of unsteady incompressible flow past a cylinder - Sensitivity of the computed flow field to the location of the outflow boundary

The influence of the location of the outflow computational boundary on the unsteady incompressible flow past a circular cylinder at Reynolds number 100 is examined. The vorticity-streamfunction formulation of the Navier-Stokes equations is used in all computations. Two types of outflow boundary conditions are subjected to a series of tests in which the domain length is gradually reduced. The traction-free condition performs well in most cases and allows the outflow boundary to be located as close as 6.5 cylinder diameters from the body. The other boundary condition type is not as forgiving, but has the advantage of being simpler to implement and can still provide reasonably accurate solutions. It is also observed that both condition types can influence the flow field strongly and globally when the boundary is brought closer than 2.5 diameters from the body. In such cases the temporal periodicity of the solution is lost.

Behr, M.↗

NASA NTRS1991

On the downstream boundary conditions for the vorticity-stream function formulation of two-dimensional incompressible flows

Downstream boundary conditions equivalent to the homogeneous form of the natural boundary conditions associated with the velocity-pressure formulation of the Navier-Stokes equations are derived for the vorticity-stream function formulation of two-dimensional incompressible flows. Of particular interest are the zero normal and shear stress conditions at a downstream boundary.

Tezduyar, T. E.↗

NASA NTRS1990

Solution techniques for the vorticity-streamfunction formulation of two-dimensional unsteady incompressible flows

A review of the solution techniques of Tezduyar et al. (1988 and 1989) for the vorticity-streamfunction formulation of two-dimensional incompressible flows is presented. While both the viscous and inviscid cases are considered, the derivation of the proper finite-element formulations for multiply connected domains is emphasized. In all formulations associated with the vorticity transport equation, the streamline upwind/Petrov-Galerkin method is used. The adaptive implicit-explicit and grouped element-by-element solution strategies are employed to maximize the computational efficiency. The solutions obtained in all test cases compare well with solutions from previously published investigations. The convergence and benchmark studies performed in this paper show that the solution techniques presented are accurate, reliable, and efficient.

Tezduyar, T. E.↗

NASA NTRS1990

Incompressible flow computations based on the vorticity-stream function and velocity-pressure formulations

Finite element procedures and computations based on the velocity-pressure and vorticity-stream function formulations of incompressible flows are presented. Two new multistep velocity-pressure formulations are proposed and compared with the vorticity-stream function and one-step formulations. The example problems chosen are the standing vortex problem and flow past a circular cylinder. Benchmark quality computations are performed for the cylinder problem. The numerical results indicate that the vorticity-stream function formulation and one of the two new multistep formulations involve much less numerical dissipation than the one-step formulation.

Tezduyar, T. E.↗

NASA NTRS1990

Combined AIE/EBE/GMRES approach to incompressible flows

Adaptive implicit-explicit (AIE), grouped element-by-element (GEBE), and generalized minimum residuals (GMRES) solution techniques for incompressible flows are combined. In this approach, the GEBE and GMRES iteration methods are employed to solve the equation systems resulting from the implicitly treated elements, and therefore no direct solution effort is involved. The benchmarking results demonstrate that this approach can substantially reduce the CPU time and memory requirements in large-scale flow problems. Although the description of the concepts and the numerical demonstration are based on the incompressible flows, the approach presented here is applicable to larger class of problems in computational mechanics.

Liou, J.↗

NASA NTRS1989

Adaptive implicit-explicit and parallel element-by-element iteration schemes

Adaptive implicit-explicit (AIE) and grouped element-by-element (GEBE) iteration schemes are presented for the finite element solution of large-scale problems in computational mechanics and physics. The AIE approach is based on the dynamic arrangement of the elements into differently treated groups. The GEBE procedure, which is a way of rewriting the EBE formulation to make its parallel processing potential and implementation more clear, is based on the static arrangement of the elements into groups with no inter-element coupling within each group. Various numerical tests performed demonstrate the savings in the CPU time and memory.

Tezduyar, T. E.↗

NASA NTRS1989

Adaptive implicit-explicit methods for flow problems

Studies on the adaptive implicit-explicit (AIE) method for large-scale problems are presented. The AIE method is based on dynamic grouping of the elements into the implicit and explicit subsets as dictated by the element level stability and accuracy considerations. The method has been applied to various flow problems including the incompressible flow and convection-diffusion problems, and it has been demonstrated that substantial savings in CPU time and memory can be achieved.

Liou, J.↗

NASA NTRS1989

Solution techniques for incompressible flow problems

A three-step Petrov-Galerkin (PG)/operator spliting scheme for the time-dependent incompressible Navier-Stokes equations is proposed. Each time step is split into two Stokes problems and one nonlinear convection-diffusion problem. Using a PG technique on the two outer Stokes problems ensures a stable scheme despite equal-order interpolation, while using a streamline upwind PG scheme on the inner convection-diffusion problem ensures a numerically stable solution at high Reynolds numbers. Numerical tests of this method have been carried out.

Tezduyar, T. E.↗

NASA NTRS1989

Finite element computations and experimental studies of flow past an array of plates

Finite element computations and laboratory experiments were carried out to study the mutual wake interaction behind two plates placed side by side. The computations are based on the vorticity-stream function formation of the two-dimensional incompressible Navier-Stokes equations. The flow visualization studies indicate independent vortex sheddings at large gap sizes and metastable biased flow at smaller gap sizes. The computational results exhibit a similar behavior.

Higuchi, H.↗

NASA NTRS1988

Element-by-element and implicit-explicit finite element formulations for computational fluid dynamics

Preconditioner algorithms to reduce the computational effort in FEM analyses of large-scale fluid-dynamics problems are presented. A general model problem is constructed on the basis of the convection-diffusion equation and the two-dimensional vorticity/stream-function formulation of the Navier-Stokes equations; this problem is then analyzed using element-by-element, implicit-explicit, and adaptive implicit-explicit approximation schemes. Numerical results for the two-dimensional advection and rigid-body rotation of a cosine hill, flow past a circular cylinder, and driven cavity flow are presented in extensive graphs and shown to be in good agreement with those obtained using implicit methods.

Tezduyar, T. E.↗

NASA NTRS1988

Adaptive implicit-explicit finite element algorithms for fluid mechanics problems

The adaptive implicit-explicit (AIE) approach is presented for the finite-element solution of various problems in computational fluid mechanics. In the AIE approach, the elements are dynamically (adaptively) arranged into differently treated groups. The differences in treatment could be based on considerations such as the cost efficiency, the type of spatial or temporal discretization employed, the choice of field equations, etc. Several numerical tests are performed to demonstrate that this approach can achieve substantial savings in CPU time and memory.

Tezduyar, T. E.↗

NASA NTRS1987

Finite element solution techniques for large-scale problems in computational fluid dynamics

Element-by-element approximate factorization, implicit-explicit and adaptive implicit-explicit approximation procedures are presented for the finite-element formulations of large-scale fluid dynamics problems. The element-by-element approximation scheme totally eliminates the need for formation, storage and inversion of large global matrices. Implicit-explicit schemes, which are approximations to implicit schemes, substantially reduce the computational burden associated with large global matrices. In the adaptive implicit-explicit scheme, the implicit elements are selected dynamically based on element level stability and accuracy considerations. This scheme provides implicit refinement where it is needed. The methods are applied to various problems governed by the convection-diffusion and incompressible Navier-Stokes equations. In all cases studied, the results obtained are indistinguishable from those obtained by the implicit formulations.

Liou, J.↗