Computational/Modeling Techniques & Verification/Validation

Numerous aspects related to computational techniques, based on Navier-Stokes and lattice Boltzmann formulations, single- and multi-phase flows, and fluid-structural interactions considerations, have been investigated. In addition, complex geometry,  high order and low dispersion/dissipation schemes, code verification techniques, and turbulence modeling have also been studied.

1. Shape-Conforming Navier-Stokes Solution Techniques

The Navier-Stokes equations along with the mass, continuity, energy, species and turbulence transport model equations are solved utilizing the pressure-based algorithm. The approach employs combined cartesian and contravariant velocity variables to facilitate strong conservation law formulations and consistent finite volume treatment. A wide variety of steady and time dependent flow problems, ranging from incompressible to hypersonic regimes have been computed using this overall framework. For problems involving moving boundaries, a moving grid technique employing the master-slave concept is used to re-mesh the multi-block structured grid for fluid-structure interaction problems. The geometric conservation law (GCL) is incorporated to compute the cell volume in a moving boundary problem consistently and eliminate the artificial mass sources.

2. Cartesian Grid Techniques

This approach is particularly suitable for multiphase flow problems invoving substantial shape deformation or even topological changes due to merger and break-up of the objects. Specifically, the flow computations are performed on a Cartesian grid that dynamically adapts itself based on the interface location and solution features. A staggered grid, finite volume formulation is used for the flow computation using a projection method. Furthermore, we have developed
(i) an integrated three-dimensional computational capability for interfacial flow involving topological changes such as break-up and coalescence,
(ii) a triangulated surface-based interface tracking with a mass-conserving technique to control the interface resolution and an improved level-contour reconstruction to better handle the topology changes,
(iii) a dynamically adaptive Cartesian grid technique with staggered grid computation for incompressible two-phase flows with disparate length scale variations.

3. Lattice Boltzmann Method

The method of lattice Boltzmann equation (LBE) is a kinetic-based approach for fluid flow computations. As a computational tool, the Navier-Stokes equations are 2nd order PDE’s while the discrete velocity model from which the LBE model is derived consists of a set of first order PDE’s.  Furthermore, the LBE method totally avoids the nonlinear convective term, because the convection becomes simple advection. It is also intrinsically easier to parallelize in computational implementation. Recent developments include the study of force evaluation methods, the development of multi-block methods which provide a means to satisfy different resolution requirement in the near wall region and the far field and reduce the memory requirement and computational time, the progress in constructing the second-order boundary condition for curved solid wall, and the multiphase, variable density flow computations.

  1. Shyy, W. (author), "Computational Modeling for Fluid Flow and Interfacial Transport", Elsevier, Amsterdam, The Netherlands, (1994, revised printing 1997); Dover, New York, 2006.
  2. Shyy, W., Udaykumar, H.S., Rao, M.M. and Smith, R.W. (authors), "Computational Fluid Dynamics with Moving Boundaries", Taylor & Francis, Washington, DC, (1996, revised printing 1997, 1998&2001); Dover, New York, 2007.
  3. Shyy, W., Thakur, S.S., Ouyang, H., Liu, J. and Blosch, E. (authors), "Computational Techniques for Complex Transport Phenomena", Cambridge University Press, New York, (1997, paperback 2005).
  4. Prewitt, N., Belk, D. and Shyy, W., "Parallel Computing of Overset Grids for Aerodynamic Problems with Moving Objects", Progress in Aerospace Sciences, Vol. 36, (2000), pp. 117-172.
  5. Garbey, M. and Shyy, W., "A Least Square Extrapolation Method for Improving Solution Accuracy of PDE Computations", Journal of Computational Physics, Vol. 186, (2003), pp. 1-23.
  6. Yu, D., Mei, R., Luo, L. and Shyy, W., "Viscous Flow Computations with the Method of Lattice Boltzmann Equation"Progress in Aerospace Sciences, Vol. 39, (2003), pp. 329-367.
  7. Kamakoti, R. and Shyy, W., "Fluid-Structure Interaction for Aeroelastic Applications", Progress in Aerospace Sciences, Vol. 40, (2004), pp. 535-558.
  8. Popescu, M., Shyy, W. and Garbey, M., "Finite Volume Treatment of Dispersion-Relation-Preserving and Optimized Prefactored Compact Schemes for Wave Equations", Journal of Computational Physics, Vol. 210, (2005), pp. 705-729.
  9. Singh, R.K. and Shyy, W., "Three-Dimensional Adaptive Cartesian Grid Method with Conservative Interface Restructuring and Reconstruction", Journal of Computational Physics, 224 (2007) 150-167
  10. Uzgoren, E., R. Singh, J. Sim, and W. Shyy, "Computational modeling for multiphase flows with spacecraft application. Progress in Aerospace Sciences, 2007, 43:138-192