WENO-TCD Scheme with LES and Reaction Capability
The purpose of the WENO-TCD
[solver] is to integrate a fluid dynamics solver that brings together the numerical requirements of simulating flows with strong shocks/discontinuities and turbulence. In the first case, unresolvable discontinuities are handled by shock capturing methods. In the second case, the turbulent regions can only be computed accurately using low dissipation (zero if possible) numerical methods. This is accomplished by upwinding the derivatives around discontinuities and using centered schemes around the turbulent regions of the flow. The current solver uses a switched paradigm, in which a user defined criteria determines when to use a centered or upwind method. Additionaly, we implement the solver as a flux based method
that enables switching numerical schemes mantaining discrete conservation (important in order to compute the correct speed of discontinuities). Related papers are:
- Hill & Pullin (2004), "Hybrid tuned center difference - WENO method for Large-Eddy Simulation in the presence of strong shocks", Journal of Computational Physics, 194(2), 435-450.
The scheme is defined by the 5 point stensil formula
%\[ \frac{d f}{d x} = \frac{1}{h} \big(\beta(f_{i+1}-f_{i-1})+\alpha (f_{i+2}-f_{i-2}) \big)\]%
where %$ \beta = 1/2-2 \alpha $% and %$\alpha=-0.197$%. This value of %$\alpha$% is obtained by minimizing the truncation errors that result for flows with a Kolmogorov-like spectra.
- Liu, Osher & Chan (1994) "Weighted essenctially nonoscillatory schemes", Journal of Computational Physics, 115(1), 200-212.
- Misra & Pullin (1997) "A vortex-based subgrid model for large-eddy simulation", Physics of Fluids, 9(8), 2443-2454.
- Pullin (2000) "Vortex-based model for subgrid flux of a passive scalar", Physics of Fluids, 12(9), 2311-2319.
- Pantano, Deiterding, Hill & Pullin (2005), "A low-numerical dissipation patched-based adaptive mesh refinement method for large-eddy simulation of compressible flows", Journal of Computational Physics (submitted).
A sample
animation of evolution a Richtmyer-Meshkov instablity between air and SF6 following a single Mach 1.5 shock interaction shows the subsequent turbulent mixing that the WENO-TCD patch
solver can efficiently compute with LES.
Conservation
Conservation is ensured by utilizing a conservative flux based approach with consistently embeded domain gridding. This technique is analogous to the zonal approach used in finite difference formulations.
Characteristic based boundary conditions are implemented for reacting mixtures. The solver follows the approach of Thomson.
Time integration
Third order Runge-Kutta schemes are used to integrate the governing equations. Currently there are two schemes implemented, a clasical scheme and the SSP scheme of Gotlieb. This last scheme is preferable when simulating flows that involve shocks.
Nonlinear stability and aliasing errors
The scientific community has learned from experience that nonlinear stability and aliasing errors become important issues when integrating the Navier-Stokes equations with low dissipation schemes for turbulent flows. In general it has been learned that stable schemes must be written in kinetic energy conservation form. The fluxes produced by the TCD scheme have been written in kinetic energy conservative form to ensure long time stability and to minimize aliasing errors by deriving the consistent fluxes from the skew-symmetric finite difference formulas.
AMR fine-coarse grid interface stability
Currently, fine-coarse mesh interface stability is ensured by utilizing the WENO fluxes in the neightbouring cells to the interface. The small and controlled amount of numerical dissipation introduced by the WENO discretization has proven to be quite effective in ensuring stability, conservation and smooth solution.
Subgrid turbulence model
The solver implements the subgrid stretched vortex model of Pullin for tranport and an assumed PDF model for nonpremixed combustion.
A new flexible module has been created to enable the user to extract almost general statistical
or samples from the AMR simulation. The module is build around the Interpolation object and allows
arbitrary sampling of data. Follow the link for a more detailed description.
The link above list the status of all the applications, from 1D to 3D. Information about the status of the
code, compilation and results are listed as they become available. The different problems represent Verification
and Validation (V&V) efforts of the compressible solver. The cases also indicate the primary developer responsible
for the case.
As new features are constantly being implemented and tested, it occasionally can lead to reverting
the code to unstable/untested state until we have the time to verify the results. Also note that it takes
time for us to verify most 3D cases.
Large-eddy simulation and Shell solver Supersonic Parachute Simulations
The development of new entry-descent-landing sequences for planned heavy payloads to be sent to Mars requires the use of new supersonic parachutes. Our understanding of the performance of these supersonic disk-gap-band (DGB) parachutes is limited. We use high-performance three-dimensional coupled large-eddy and finite-deformation structural dynamics simulation to aide in the development of these new systems. The objective is to improve our understanding of the multiple stability domains and performance parameters, drag, lateral forces and structural loading, of the parachute-payload system in the entry, descent and landing sequence of Mars missions. To aide in mission design and planning, we use the VTF, including: large-eddy simulation, compressible subgrid scale modeling, shock capturing, finite element modeling of the parachute canopy and the suspension lines, adaptive mesh refinement, dynamic error control and parallelization. The VTF run on massively parallel high-performance computers, such as the JPL's Cosmos and Altix clusters, and is aiding in the risk assessment and design of upcoming NASA missions and, in the long term, guide the design of new more aggressive parachute systems with novel canopy configurations or unfolding sequences.
FlexPara-M1.96-Case21-2x.mpg