AMR for Incompressible Flow ModelingModeling of incompressible and low-speed flows has become one of the cornerstones of the simulation capability of the Center for Computational Sciences and Engineering (CCSE). This capability has been the springboard for CCSE's combustion modeling capability, as well as useful in itself for explorations of incompressible, nonreacting turbulent flow, as shown below. The algorithmic complexity of AMR algorithms is significantly higher for low-speed as opposed to fully compressible flows. The equations of inviscid gas dynamics are systems of conservation laws, purely hyperbolic in character. The equations governing incompressible flow, by contrast, include hyperbolic equations governing advection, parabolic equations for the Crank-Nicolson discretization of diffusing quantities, and elliptic equations to enforce the velocity divergence constraint. The method we use to solve these equations is based on a projection formulation in which we first solve advection-diffusion equations to predict intermediate velocities, and then project these velocities onto a space of approximately divergence-free vector fields. Our treatment of the first step uses a specialized second-order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high Reynolds number flow. Density and other scalars are advected in such a way as to maintain conservation, if appropriate, and free-stream preservation. Implicit Large Eddy Simulation
More information can be found here... Please direct any questions to Andy Aspden. Turbulent Jets with Off-Source Heating
More information can be found here... Please direct any questions to Andy Aspden. Three-dimensional Variable Density Incompressible Shear LayerOne of our early calculations using the IAMR methodology was of a time-evolving three-dimensional variable density shear layer. The figure here is a three-dimensional rendering of vorticity; green is the maximum value, and the background black is the absence of vorticity. The problem specification models the classic experiments performed by Brown and Roshko (1974) to study the effects of density variation on low speed shear layers. We can see the essentially two-dimensional roll-up of the vortex sheet as well as the spanwise structure induced by a three-dimensional perturbation of the inflow data designed to mimic a mild "flutter" of the splitter plate used in experiments. Although the grids are not shown in this image, this calculation was performed adaptively, on a DEC Alpha workstation. In this calculation the density interface and subsequent roll-up are captured at the finest resolution, while the regions near the boundary are at coarser resolution. The computational results were in agreement with experimental data for both the visual spreading rate and the mean profiles of velocity. The details of the calculation, and the method used to generate it, are described in the reference below. The IAMR code which generated the results is publicly available. If you are interested in using this code, please contact Ann Almgren of CCSE.ReferenceA. S. Almgren, J. B. Bell, P. Colella, L. H. Howell, and M. L. Welcome, ``A Conservative Adaptive Projection Method for the Variable Density Incompressible Navier-Stokes Equations,'', J. Comp. Phys., 142, pp. 1-46, 1998. [ps.gz] |