Drona Kandhai

The distributed ASCI Supercomputer project

The Distributed ASCI Supercomputer (DAS) is a homogeneous wide-area distributed system consisting of four cluster computers at different locations. DAS has been used for research on communication software, parallel languages and programming systems, schedulers, parallel applications, and distributed applications. The paper gives a preview of the most interesting research results obtained so far in the DAS project.

Lattice-Boltzmann hydrodynamics on parallel systems

Realistic lattice-Boltzmann simulations often require large amounts of computational resources and are therefore executed on parallel systems. Generally, parallelization is based on one- and two-dimensional decomposition of the computational grid in equal subvolumes, and load balancing is completely ignored for simplicity. Besides reviewing the existing parallelization strategies we report here a new approach based on the Orthogonal Recursive Bisection (ORB) method. To illustrate the different decomposition methods, two realistic applications were simulated, namely fluid flow in random fibre networks and flow in a centrifugal elutriation chamber. For heterogeneously distributed workloads, the ORB method is found to be 12 to 60% more efficient compared to traditional parallelization strategies. It is shown that high parallel efficiencies can be obtained for both homogeneously and heterogeneously distributed workloads, thus supporting efficient simulations of a variety of realistic systems.

Lattice‐Boltzmann and finite element simulations of fluid flow in a SMRX Static Mixer Reactor

SUMMARY A detailed comparison between the finite element method (FEM) and the lattice-Boltzmann method (LBM) is presented. As a realistic test case, three-dimensional fluid flow simulations in an SMRX static mixer were performed. The SMRX static mixer is a piece of equipment with excellent mixing performance and it is used as a highly efficient chemical reactor for viscous systems like polymers. The complex geometry of this mixer makes such three-dimensional simulations non-trivial. An excellent agreement between the results of the two simulation methods was found. Furthermore, the numerical results for the pressure drop as a function of the flow rate were close to experimental measurements. Results show that the relatively simple LBM is a good alternative to traditional methods. Copyright

Shear-induced self-diffusion and microstructure in non-brownian suspensions at non-zero Reynolds numbers

This paper addresses shear-induced self-diffusion in a monodisperse suspension of non-Brownian particles in Couette flow by two-dimensional computer simulations following the lattice-Boltzmann method. This method is suited for the study of (many-particle) particulate suspensions and can not only be applied for Stokes flow, but also for flow with finite Reynolds number. At relatively low shear particle Reynolds numbers (up to 0.023), shear-induced diffusivity exhibited a linear dependence on the shear rate, as expected from theoretical considerations. Simulations at shear particle Reynolds numbers between 0.023 and 0.35, however, revealed that in this regime, shear-induced diffusivity did not show this linear dependence anymore. Instead, the diffusivity was found to increase more than linearly with the shear rate, an effect that was most pronounced at lower area fractions of 0.10 and 0.25. In the same shear regime, major changes were found in the flow trajectories of two interacting particles in shear flow (longer and closer approach) and in the viscosity of the suspension (shear thickening). Moreover, the suspended particles exhibited particle clustering. The increase of shear-induced diffusivity is shown to be directly correlated with this particle clustering. As for shear-induced diffusivity, the effect of increasing shear rates on particle clustering was the most intensive at low area fractions of 0.10 and 0.25, where the radius of the clusters increased from about 4 to about 7 particle radii with an increase of the shear Reynolds number from 0.023 to 0.35. The importance of particle clustering to shear-induced diffusion might also indicate the importance of other factors that can induce particle clustering, such as, for example, colloidal instability.

Finite-Difference Lattice-BGK Methods on Nested Grids

From a computational point of view non uniform grids can be efficient for computing fluid flows because the grid resolution can be adapted to the spatial complexity of the flow problem. In this contribution an extension of the Finite-Difference Lattice-BGK method on nested grids is presented. This approach is based on multiple nested lattices with increasing resolution. Basically, the discrete velocity Boltzmann equation is solved numerically on each sub-lattice and interpolation between the interfaces is carried out in order to couple the sub-grids consistently. Preliminary results of the method applied on the Taylor vortex benchmark are presented.

Simulations of Single-Fluid Flow in Porous Media

Several results of lattice-gas and lattice-Boltzmann simulations of single-fluid flow in 2D and 3D porous media are discussed. Simulation results for the tortuosity, effective porosity and permeability of a 2D random porous medium are reported. A modified Kozeny–Carman law is suggested, which includes the concept of effective porosity. This law is found to fit well the simulated 2D permeabilities. The results for fluid flow through large 3D random fibre webs are also presented. The simulated permeabilities of these webs are found to be in good agreement with experimental data. The simulations also confirm that, for this kind of materials, permeability depends exponentially on porosity over a large porosity range.

Lattice BGK simulations of flow in a symmetric bifurcation

Surgical planning as a treatment for vascular diseases requires fast blood flow simulations that are efficient in handling changing geometry. It is, for example, necessary to try different paths of a planned bypass and study the resulting hemodynamic flow fields before deciding the final geometrical solution. With the aid of a real time interactive simulation environment that uses an efficient flow solver, this allows flexible treatment planning. In this article, we demonstrate that the lattice Boltzmann method can be an alternative robust computational fluid dynamics technique for such kind of applications. Steady flow in a 2D symmetric bifurcation is studied and the obtained flow fields and stress tensor components are compared to those obtained by a Navier-Stokes (NS) solver. We also demonstrate that the method is fully adaptive to interactively changing geometry.

Numerical simulation and measurement of liquid hold-up in biporous media containing discrete stagnant zones

We have studied hydrodynamic dispersion in single–phase incompressible liquid flow through a fixed bed made of spherical, permeable (porous) particles. The observed behaviour was contrasted with the corresponding fluid dynamics in a random packing of impermeable (non–porous) spheres with an interparticle void fraction of 0.37. Experimental data were obtained in the laminar flow regime by pulsed field gradient nuclear magnetic resonance and were complemented by numerical simulations employing a hierarchical transport model with a discrete (lattice Boltzmann) interparticle flow field. Finite–size effects in the simulation associated with the spatial discretization of support particles or dimension and boundaries of the bed were minimized and the simulation results are in reasonable agreement with experiment.

A comparison between lattice-boltzmann and finite element simulations of fluid flow in static mixer reactors

We present a comparison between the finite-element and the lattice-Boltzmann method for simulating fluid flow in a SMRX static mixer reactor. The SMRX static mixer is a piece of equipment with excellent mixing performance and it is used in highly efficient chemical reactors for viscous systems like polymers. The complex geometry of this mixer makes such 3D simulations nontrivial. An excellent agreement between the results of the two simulation methods and experimental data was found.

EFFICIENT COMPUTATION OF EXPOSURE PROFILES FOR COUNTERPARTY CREDIT RISK

Three computational techniques for approximation of counterparty exposure for financial derivatives are presented. The exposure can be used to quantify so-called Credit Valuation Adjustment (CVA) and Potential Future Exposure (PFE), which are of utmost importance for modern risk management in the financial industry, especially since the recent credit crisis. The three techniques all involve a Monte Carlo path discretization and simulation of the underlying entities. Along the generated paths, the corresponding values and distributions are computed during the entire lifetime of the option. Option values are computed by either the finite difference method for the corresponding partial differential equations, or the simulation-based Stochastic Grid Bundling Method (SGBM), or by the COS method, based on Fourier-cosine expansions. In this research, numerical results are presented for early-exercise options. The underlying asset dynamics are given by either the Black–Scholes or the Heston stochastic volatility model.