S. Aliabadi

Flow simulation and high performance computing

Flow simulation is a computational tool for exploring science and technology involving flow applications. It can provide cost-effective alternatives or complements to laboratory experiments, field tests and prototyping. Flow simulation relies heavily on high performance computing (HPC). We view HPC as having two major components. One is advanced algorithms capable of accurately simulating complex, real-world problems. The other is advanced computer hardware and networking with sufficient power, memory and bandwidth to execute those simulations. While HPC enables flow simulation, flow simulation motivates development of novel HPC techniques. This paper focuses on demonstrating that flow simulation has come a long way and is being applied to many complex, real-world problems in different fields of engineering and applied sciences, particularly in aerospace engineering and applied fluid mechanics. Flow simulation has come a long way because HPC has come a long way. This paper also provides a brief review of some of the recently-developed HPC methods and tools that has played a major role in bringing flow simulation where it is today. A number of 3D flow simulations are presented in this paper as examples of the level of computational capability reached with recent HPC methods and hardware. These examples are, flow around a fighter aircraft, flow around two trains passing in a tunnel, large ram-air parachutes, flow over hydraulic structures, contaminant dispersion in a model subway station, airflow past an automobile, multiple spheres falling in a liquid-filled tube, and dynamics of a paratrooper jumping from a cargo aircraft.

SUPG finite element computation of compressible flows with the entropy and conservation variables formulations

Abstract SUPG-stabilized finite element formulations of compressible Euler equations based on the conservation and entropy variables are investigated and compared. The formulation based on the conservation variables consists of the formulation introduced by Tezduyar and Hughes plus a shock capturing term. The formulation based on the entropy variables is the same as the one by Hughes, Franca and Mallet, which has a shock capturing term built in. These formulations are tested on several subsonic, transonic and supersonic compressible flow problems. It is shown that the stabilized formulation based on the conservation variables gives solutions which are just as good as those obtained with the entropy variables. Furthermore, the solutions obtained using the two formulations are very close and in some cases almost indistinguishable. Consequently, it can be deduced that the relative merits of these two formulations will continue to remain under debate.

Massively parallel finite element simulation Of compressible and incompressible flows

We present a review of where our research group stands in parallel finite element simulation of flow problems on the Connection Machines, an effort that started for our group in the fourth quarter of 1991. This review includes an overview of our work on computation of flow problems involving moving boundaries and interfaces, such as free surfaces, two-liquid interfaces, and fluid-structure and fluid-particle interactions. With numerous examples, we demonstrate that, with these new computational capabilities, today we are at a point where we routinely solve practical flow problems, including those in 3D and those involving moving boundaries and interfaces. We solve these problems with unstructured grids and implicit methods, with some of the problem sizes exceeding 5 000 000 equations, and with computational speeds up to two orders of magnitude higher than what was previously available to us on the traditional vector supercomputers.

Space-time finite element computation of compressible flows involving moving boundaries and interfaces

Abstract The deformable-spatial-domain/stabilized-space-time (DSD/SST) formulation, introduced by Tezduyar et al. is applied to computation of viscous compressible flows involving moving boundaries and interfaces. The stabilization technique employed is a streamline-upwind/Petrov-Galerkin (SUPG) method, with a modified SUPG stabilization matrix. The stabilized finite element formulation of the governing equations is written over the space-time domain of the problem, and therefore the deformation of the spatial domain with respect to time is taken into account automatically. The frequency of remeshing is minimized to minimize the projection errors involved in remeshing and also to increase the parallelization potential of the computations. The implicit equation systems arising from the space-time finite element discretizations are solved iteratively. It is demonstrated that the combination of the SUPG stabilization and the space-time approach gives the capability of handling complicated compressible flow problems, including those with moving surfaces and shock-boundary layer interactions.

Enhanced-Discretization Interface-Capturing Technique (EDICT) for computation of unsteady flows with interfaces

Abstract We present the Enhanced-Discretization Interface-Capturing Technique (EDICT) for computation of unsteady flow problems with interfaces, such as two-fluid and free-surface flows. In EDICT, we solve, over a non-moving mesh, the Navier-Stokes equations together with an advection equation governing the evolution of an interface function with two distinct values identifying the two fluids. The starting point for the spatial discretization of these equations are the stabilized finite element formulations which possess good stability and accuracy properties. To increase the accuracy in modeling the interfaces, we use finite element functions corresponding to enhanced discretization at and near the interface. These functions are designed to have multiple components, with each component coming from a different level of mesh refinement over the same computational domain. The primary component of the functions for velocity and pressure comes from the base mesh called Mesh-1. A subset of the elements in Mesh-1 are identified to be at or near the interface, and depending on where the interface is, this subset could change from one time level to another. A Mesh-2 is constructed by patching together the second-level meshes generated over this subset of elements, and the second component of the functions for velocity and pressure comes from Mesh-2. For the interface function, we have a third component coming from a Mesh-3 which is constructed by patching together the third-level meshes generated over a subset of elements in Mesh-2. With parallel computation of the test problems presented here, we demonstrate that the EDICT can be used very effectively to increase the accuracy of the base finite element formulations.

Comparison of finite element and pendulum models for simulation of sloshing

Abstract The pendulum model is a cost effective tool for the simulation of sloshing. However, the accuracy and applicability of the model has not been well established. In this article, we compare the simulation results obtained from the pendulum model and a more complicated finite element model for sloshing of liquids in tanker trucks. In the pendulum model, we assume that the liquid in the tanker is a point mass oscillating like a frictionless pendulum subjected to an external acceleration. In the finite element model, we solve the full Navier–Stokes equations written for two fluids to obtain the location and motion of the free surface. Stabilized finite element formulations are used in these complex 3D simulations. These finite element formulations are implemented in parallel using the message-passing interface libraries. The numerical example includes the simulation of sloshing in tanker trucks during turning.

Stabilized-finite-element/interface-capturing technique for parallel computation of unsteady flows with interfaces

We present the stabilized-finite-element/interface-capturing (SFE/IC) method developed for parallel computation of unsteady flow problems with two-fluid interfaces and free surfaces. The SFE/IC method involves stabilized formulations, an interface-sharpening technique, and the enforcement of global mass conservation for each fluid. The SFE/IC method has been efficiently implemented on the CRAY T3E parallel supercomputer. A number of 2D test problems are presented to demonstrate how the SFE/IC method works and the accuracy it attains. We also show how the SFE/IC method can be very effectively applied to 3D simulation of challenging flow problems, such as two-fluid interfaces in a centrifuge tube and operational stability of a partially filled tanker truck driving over a bump.

SUPG finite element computation of viscous compressible flows based on the conservation and entropy variables formulations

In this article, we present our investigation and comparison of the SUPG-stabilized finite element formulations for computation of viscous compressible flows based on the conservation and entropy variables. This article is a sequel to the one on inviscid compressible flows by Le Beau et al. (1992). For the conservation variables formulation, we use the SUPG stabilization technique introduced in Aliabadi and Tezduyar (1992), which is a modified version of the one described in Le Beau et al. (1992). The formulation based on the entropy variables is same as the one introduced in Hughes et al. (1986).The two formulations are tested on three different problems: adiabatic flat plate at Mach 2.5, Reynolds number 20,000; Mach 3 compression corner at Reynolds number 16,800; and Mach 6 NACA 0012 airfoil at Reynolds number 10,000. In all cases, we show that the results obtained with the two formulations are very close. This observation is the same as the one we had in Le Beau et al. (1992) for inviscid flows.

A new mixed preconditioning method for finite element computations

A new mixed clustered element-by-element (CEBE)/cluster companion (CC) preconditioning method for finite element computations is introduced. In the CEBE preconditioning, the elements are merged into clusters of elements, and the preconditioners are defined as series products of cluster level matrices. The CC preconditioning method, which is also introduced in this paper, shares a common philosophy with the multi-grid methods. The CC preconditioners are based on companion meshes associated with different levels of clustering. For each level of clustering, we construct a CEBE preconditioner and an associated CC preconditioner. Because these two preconditioners in a sense complement each other, when they are used in a mixed way, they can be expected to give better performance. In fact, our numerical tests, for two- and three-dimensional problems governed by the Poisson equation, demonstrate that the mixed CEBE/CC preconditioning results in convergence rates which are, in most cases, significantly better than the convergence rates obtained with the best of the CEBE and CC preconditioning methods.

EDICT for 3D computation of two-fluid interfaces

Abstract We present the 3D implementation and applications of the enhanced-discretization interface-capturing technique (EDICT) in computation of unsteady flows with two-fluid interfaces. In such computations, EDICT can be used as a very effective method, which combines the flexibility and efficiency of interface-capturing techniques with the accuracy provided by enhanced discretization at the interfaces. A stabilized finite element interface-capturing technique is used as the base formulation to solve, over a typically non-moving mesh, the Navier–Stokes equations and an advection equation governing the interface function. To increase the accuracy in modeling the interfaces, we use finite element functions with multiple components at and near the interfaces, with each component coming from a different level of mesh refinement. With its parallel implementation on advanced high-performance computing platforms such as the CRAY T3E, EDICT is a powerful tool for the simulation of a complex, 3D unsteady flow problems with two fluid-interfaces, including free surfaces.