Frank Ham

Liszt: a domain specific language for building portable mesh-based PDE solvers

Heterogeneous computers with processors and accelerators are becoming widespread in scientific computing. However, it is difficult to program hybrid architectures and there is no commonly accepted programming model. Ideally, applications should be written in a way that is portable to many platforms, but providing this portability for general programs is a hard problem. By restricting the class of programs considered, we can make this portability feasible. We present Liszt, a domain- specific language for constructing mesh-based PDE solvers. We introduce language statements for interacting with an unstructured mesh, and storing data at its elements. Pro- gram analysis of these statements enables our compiler to expose the parallelism, locality, and synchronization of Liszt programs. Using this analysis, we generate applications for multiple platforms: a cluster, an SMP, and a GPU. This approach allows Liszt applications to perform within 12% of hand-written C++, scale to large clusters, and experience order-of-magnitude speedups on GPUs.

Large-Eddy Simulation of Reacting Turbulent Flows in Complex Geometries

Large-eddy simulation (LES) has traditionally been restricted to fairly simple geometries. This paper discusses LES of reacting flows in geometries as complex as commercial gas turbine engine combustors. The incompressible algorithm developed by Mahesh et al. (J. Comput. Phys., 2004, 197, 215-240) is extended to the zero Mach number equations with heat release. Chemical reactions are modeled using the flamelet/progress variable approach of Pierce and Moin (J. Fluid Mech., 2004, 504, 73-97). The simulations are validated against experiment for methane-air combustion in a coaxial geometry, and jet-A surrogate/air combustion in a gas-turbine combustor geometry.

Reynolds-Averaged Navier-Stokes Simulations of the HyShot II Scramjet

The internal flow in the HyShot II scramjet is investigated through numerical simulations. A computational infrastructure to solve the compressible Reynolds-averaged Navier–Stokes equations on unstructured meshes is introduced. A combustion model based on tabulated chemistry is considered to incorporate detailed chemical– kinetics mechanics while retaining a low computational cost. Both nonreactive and reactive simulations have been performed, and results are compared with ground test measurements obtained at DLR, German Aerospace Center. Different turbulence models were tested, and the dependence on the mesh is assessed through grid refinement. The comparison with experimental data shows good agreement, although the computed heat fluxes at the wall are higher thanmeasurements for the reactive case. A sensitivity analysis on the turbulent Schmidt and Prandtl numbers shows that the choice of these parameters has a strong influence on the results. In particular, variations of the turbulent Prandtl number lead to large changes in the heat flux at the walls. Finally, the inception of thermal choking is investigated by increasing the equivalence ratio, whereby a normal shock is created locally and moves upstream, leading to a large increase in the maximum pressure. Nevertheless, a large portion of the flow is still supersonic.

Stable and accurate wave-propagation in discontinuous media

A time stable discretization is derived for the second-order wave equation with discontinuous coefficients. The discontinuity corresponds to inhomogeneity in the underlying medium and is treated by splitting the domain. Each (homogeneous) sub domain is discretized using narrow-diagonal summation by parts operators and, then, patched to its neighbors by using a penalty method, leading to fully explicit time integration. This discretization yields a time stable and efficient scheme. The analysis is verified by numerical simulations in one-dimension using high-order finite difference discretizations, and in three-dimensions using an unstructured finite volume discretization.

Prediction of Sound Generated by Complex Flows at Low Mach Numbers

We present a computational aeroacoustics method to evaluate sound generated by low Mach number flows in complex configurations in which turbulence interacts with arbitrarily shaped solid objects. This hybrid approach is based on Lighthills acoustic analogy in conjunction with sound source information from an incompressible calculation. In this method, Lighthills equation is solved using a boundary element method that allows the effect of scattered sound from arbitrarily shaped solid objects to be incorporated. We present validation studies for sound generated by laminar and turbulent flows over a circular cylinder at Re = 100 and 10,000, respectively. Our hybrid approach is validated against directly computed sound using a high-order compressible flow solver as well as the solution of the Ffowcs Williams and Hawkings equation in conjunction with compressible sound sources. We demonstrate that the sound predicted by a second-order hybrid approach is as accurate as sound directly computed by a sixth-order compressible flow solver in the frequency range in which low-order numerics can accurately resolve the flow structures. As an example of an engineering problem, we calculated the sound generated by flow over an automobile side-view mirror and compared it to experimental measurements.

Discrete conservation principles in large-eddy simulation with application to separation control over an airfoil

An unstructured-grid large-eddy simulation (LES) technique is used to investigate the turbulent flow separation over an airfoil with and without synthetic-jet control. Numerical accuracy and stability on arbitrary shaped mesh elements at high Reynolds numbers are achieved using a finite-volume discretization of the incompressible Navier–Stokes equations based on higher-order conservation principles—i.e., in addition to mass and momentum conservation, kinetic energy conservation in the inviscid limit is used to guide the selection of the discrete operators and solution algorithm. Two different stall configurations, which consist of flow over a NACA 0015 airfoil at 16.6° and 20° angles of attack, are simulated at Reynolds number of 896 000 based on the airfoil chord length and freestream velocity. In the case of 16.6° angle of attack where flow separates around a midchord location, LES results show excellent agreement with the experimental data for both uncontrolled and controlled cases. LES confirms the ex...

Prediction of wall-pressure fluctuation in turbulent flows with an immersed boundary method

The objective of this paper is to assess the accuracy and efficiency of the immersed boundary (IB) method to predict the wall pressure fluctuations in turbulent flows, where the flow dynamics in the near-wall region is fundamental to correctly predict the overall flow. The present approach achieves sufficient accuracy at the immersed boundary and overcomes deficiencies in previous IB methods by introducing additional constraints - a compatibility for the interpolated velocity boundary condition related to mass conservation and the formal decoupling of the pressure on this surfaces. The immersed boundary-approximated domain method (IB-ADM) developed in the present study satisfies these conditions with an inexpensive computational overhead. The IB-ADM correctly predicts the near-wall velocity, pressure and scalar fields in several example problems, including flows around a very thin solid object for which incorrect results were obtained with previous IB methods. In order to have sufficient near-wall mesh resolution for LES and DNS computations, the present approach uses local mesh refinement. The present method has been also successfully applied to computation of the wall-pressure space-time correlation in DNS of turbulent channel flow on grids not aligned with the boundaries. When applied to a turbulent flow around an airfoil, the computed flow statistics - the mean/RMS flow field and power spectra of the wall pressure - are in good agreement with experiment.

Towards best practices for jet noise predictions with unstructured large eddy simulations

Experience gained from previous jet noise studies with the unstructured large eddy simulation (LES) flow solver “Charles” are summarized and put to practice for the predictions of supersonic jets issued from a converging-diverging round nozzle. In this work, the nozzle geometry is explicitly included in the computational domain using an unstructured body-fitted mesh with 42 million cells. Three different operating conditions are considered: isothermal ideally-expanded, heated ideally-expanded and heated over-expanded. Blind comparisons with the currently available experimental measurements carried out at United Technologies Research Center for the same nozzle and operating conditions are presented. The initial results show good agreement for both flow and sound field. In particular, the spectra shape and levels are accurately captured in the simulations for both near-field and far-field noise. In these studies, sound radiation from the jet is computed using an efficient permeable formulation of the Ffowcs Williams–Hawkings equation in the frequency domain. Its implementation in Cascade’s massively-parallel unstructured LES framework is reviewed and additional parametric studies of the far-field noise predictions are presented. As an additional step towards best practices for jet aeroacoustics with unstructured LES, guidelines and suggestions for the mesh design, numerical setup and acoustic post-processing steps are discussed.

Stable Boundary Treatment for the Wave Equation on Second-Order Form

A stable and accurate boundary treatment is derived for the second-order wave equation. The domain is discretized using narrow-diagonal summation by parts operators and the boundary conditions are imposed using a penalty method, leading to fully explicit time integration. This discretization yields a stable and efficient scheme. The analysis is verified by numerical simulations in one-dimension using high-order finite difference discretizations, and in three-dimensions using an unstructured finite volume discretization.

DNS of buoyancy-dominated turbulent flows on a bluff body using the immersed boundary method

A novel immersed boundary (IB) method has been developed for simulating multi-material heat transfer problem - a cylinder in a channel heated from below with mixed convection. The method is based on a second-order velocity/scalar reconstruction near the IB. A novel algorithm has been developed for the IB method to handle conjugate heat transfer. The fluid-solid interface is constructed as a collection of disjoint faces of control volumes associated to different material zones. Coupling conditions for the material zones have been developed such that continuity and conservation of the scalar flux are satisfied by a second-order interpolation. Predictions of the local Nusselt number on the cylinder surface show good agreement with the experimental data. The effect of the Boussinesq approximation on this problem was also investigated. Comparison with the variable density formulation suggests that, in spite of a small thermal expansion coefficient of water, the variable density formulation in a transitional flow with mixed convection is preferable.