Viscous Flow Applications Research Articles

An efficient, robust and high accuracy framework for direct numerical simulation of 2D and 2D axisymmetric immiscible flow with large property contrast

We develop an efficient, robust and high accuracy framework for the direct numerical simulation of incompressible multiphase flow. This approach combines a high accuracy interfacial jump capturing method with a topology preserving interface tracking method in a semi-implicit setting. With the help of a composite solution for the individual fluid phases within the interfacial cells, the interfacial jump capturing method provides a 2nd order accurate solution and leads to a symmetric coefficient matrix. The method is fully integrated with a high accuracy, topology preserving level set based interface model that allows the accurate translation of the jump conditions between the interface and the grid cells. These two methods of interfacial jump capturing and topology preserving interface tracking are implemented within a semi-implicit solution framework to reduce the simulation cost for viscous flow applications. We solve a variety of 2D and 2D axisymmetric test problems to both verify and validate the new framework.

Lattice Boltzmann simulation for high-speed compressible viscous flows with a boundary layer

• A coupled DDF-LB model was used to simulate high-speed compressible viscous flows. • NND and second-order upwind difference schemes were compared in simulations. • The DDF-LB model could simulate a compressible boundary layer up to Ma = 6. • Local high pressure appeared with the shock wave due to LBM’s mesoscopic feature. • High potential of LBM was shown for the shock boundary layer interaction problem. In this study, the lattice Boltzmann method is employed for simulating high-speed compressible viscous flows with a boundary layer. The coupled double-distribution-function lattice Boltzmann method proposed by Li et al. (2007) is employed because of its good numerical stability and non-free-parameter feature. The non-uniform mesh construction near the wall boundary in fine grids is combined with an appropriate wall boundary treatment for the finite difference method in order to obtain accurate spatial resolution in the boundary layer problem. Three typical problems in high-speed viscous flows are solved in the lattice Boltzmann simulation, i.e., the compressible boundary layer problem, shock wave problem, and shock boundary layer interaction problem. In addition, in-depth comparisons are made with the non-oscillatory and non-free-parameter dissipation (NND) scheme and second order upwind scheme in the present lattice Boltzmann model. Our simulation results indicate the great potential of the lattice Boltzmann method for simulating high-speed compressible viscous flows with a boundary layer. Further research is needed (e.g., better numerical models and appropriate finite difference schemes) because the lattice Boltzmann method is still immature for high-speed compressible viscous flow applications.

Adaptive boundary layer meshing for viscous flow simulations

A procedure for anisotropic mesh adaptation accounting for mixed element types and boundary layer meshes is presented. The method allows to automatically construct meshes on domains of interest to accurately and efficiently compute key flow quantities, especially near wall quantities like wall shear stress. The new adaptive approach uses local mesh modification procedures in a manner that maintains layered and graded elements near the walls, which are popularly known as boundary layer or semi-structured meshes, with highly anisotropic elements of mixed topologies. The technique developed is well suited for viscous flow applications where exact knowledge of the mesh resolution over the computational domain required to accurately resolve flow features of interest is unknown a priori. We apply the method to two types of problem cases; the first type, which lies in the field of hemodynamics, involves pulsatile flow in blood vessels including a porcine aorta case with a stenosis bypassed by a graft whereas the other involves high-speed flow through a double throat nozzle encountered in the field of aerodynamics.

Thermal expansion models of viscous fluids based on limits of free energy

Many viscous flows are mechanically incompressible, yet thermally expand and shrink. Approximations of the compressible Navier–Stokes equations are routinely utilized to model diverse phenomena that share these properties, with a primary goal to remove rapid timescales associated with sound waves. Most models are derived from thermodynamic assumptions coupled with application-specific, scale separation assumptions in time and space. The Boussinesq model for laboratory-scale, buoyancy-driven thermal convection patterns [Spiegel and Veronis, Astrophys. J. 131, 442 (1960)] and the anelastic model for atmospheric-scale, density-stratification phenomena [Emanuel, Atmospheric Convection (Oxford University Press, New York, 1994)] are two important examples. Some engineering models of thermal expansion are fluid specific, e.g., for molten glasses and polymers, and rest upon thermodynamic assumptions alone. These models postpone specification of flow conditions, since applications range from slow confined flows for mold filling, to film flows, to high-speed, free surface fiber flows. The aims of this paper are to systematize the implementation of thermodynamic assumptions to derive thermal expansion models; to benchmark this class of models with respect to near-equilibrium physical behavior; and to pose candidate models for thermal expansion which may be used for a diverse set of flow conditions. By casting thermodynamic assumptions as limits of free energy, we reduce the full Navier–Stokes system in a straightforward way, and parametrize the limits of linearized compressible modes and their propagation properties. The thermodynamic assumptions are uncoupled from flow-dependent scale separation conditions, which can be subsequently augmented for specific applications. Indeed, one conclusion of this analysis is that the traditional thermal expansion assumption, where density is slaved to the temperature field, must be coupled with additional flow or thermal assumptions or else the model equations possess unphysical properties (e.g., instability of thermodynamic equilibrium or negative specific heat). Two new models for thermal expansion are deduced solely from a limit condition on free energy, which pass the minimal benchmark of non-negativity of bulk modulus, squared sound speed, and specific heat. We close with an indication of viscous flow applications of one of the new thermal expansion models.

Adaptive spatial partitioning and refinement for overset structured grids

The need for adaptive refinement for unsteady aerodynamic applications that may involve relative motion between configuration components is recognized. An efficient means of adaptive refinement within systems of overset structured grids is presented. Problem domains are segregated into near-body and off-body fields. Near-body fields are discretized via overlapping body-fitted grids that extend a short distance from body surfaces. Off-body fields are discretized via systems of overlapping uniform Cartesian (structured) grids of varying levels of refinement. A novel method of adaptive spatial partitioning and refinement that is responsive to evolving off-body flow dynamics and proximity of moving solid bodies is described. Computational advantages of structured data are reviewed. Properties of uniform Cartesian grids that lead to substantial computational advantages are identified. A grid component grouping algorithm is presented. Formal accuracy of the method is considered. The method is demonstrated for three-dimensional unsteady viscous flow applications of practical relevance.

Hybrid Prismatic/Tetrahedral Grid Generation for Viscous Flow Applications

A method for the automatic generation of unstructured grids composed of tetrahedra and prisms is proposed. The prismatic semistructured grid is generated around viscous boundary surfaces and covers viscous regions, whereas the tetrahedral grid covers the rest of the computational domain. The Delaunay approach for tetrahedral grid generation is used. The proposed prismatic grid is structured in directions normal to the boundary faces, but the number of prisms generated from one boundary face is variable from face to face. Unlike conventional prismatic grid generators, this technique works well even in regions of cavities and gaps. The Delaunay background grid generated for surface nodes serves as an efficient data structure to check possible intersections of prisms. Particular attention is given to the boundary-constraining problem. A robust algorithm for the boundary recovery by edge swapping followed by a direct subdivision of tetrahedra is used. Grid examples for internal and external flow problems of complex shapes demonstrate the efficiency of the method

Hybrid prismatic/tetrahedral grid generation for viscous flow applications

Hybrid prismatic/tetrahedral grid generation for viscous flow applications

Preconditioned Multigrid Methods for Compressible Flow Calculations on Stretched Meshes

Efficient preconditioned multigrid methods are developed for both inviscid and viscous flow applications. The work is motivated by the mixed results obtained using the standard approach of scalar preconditioning and full coarsened multigrid, which performs well for Euler calculations on moderately stretched meshes but is far less effective for turbulent Naiver–Stokes calculations, when the cell stretching becomes severe. In the inviscid case, numerical studies of the preconditioned Fourier footprints demonstrate that a block-Jacobi matrix preconditioner substantially improves the damping and propagative efficiency of Runge–Kutta time-stepping schemes for use with full coarsened multigrid, yielding computational savings of approximately a factor of three over the standard approach. In the viscous case, determination of the analytic expressions for the preconditioned Fourier footprints in an asymptotically stretched boundary layer cell reveals that all error modes can be effectively damped using a combination of block-Jacobi preconditioning and a J-coarsened multigrid strategy, in which coarsening is performed only in the direction normal to the wall. The computational savings using this new approach are roughly a factor of 10 for turbulent Navier–Stokes calculations on highly stretched meshes.

Adaptive unstructured grid generation for viscous flow applications

Our objective is to develop a procedure for efficient generation of high-quality solution-adapted grids suitable for viscous flow applications. The overall approach taken in this work for solution adaptation is to generate high-aspect-ratio elements in the boundary-layer regions and to capture inviscid features and detached viscous features independently using different adaptation procedures.