High-order Navier-Stokes Solver Research Articles

Task-parallel in situ temporal compression of large-scale computational fluid dynamics data

Present day computational fluid dynamics (CFD) simulations generate considerable amounts of data, sometimes on the order of TB/s. Often, a significant fraction of this data is discarded because current storage systems are unable to keep pace. To address this, data compression algorithms can be applied to data arrays containing flow quantities of interest (QoIs) to reduce the overall required storage. The matrix column interpolative decomposition (ID) can be implemented as a type of lossy compression for data matrices that factors the original data matrix into a product of two smaller factor matrices. One of these matrices consists of a subset of the columns of the original data matrix, while the other is a coefficient matrix which approximates the original data matrix columns as linear combinations of the selected columns. Motivating this work is the observation that the structure of ID algorithms makes them well suited for the asynchronous nature of task-based parallelism; they can operate independently on subdomains of the system of interest and, as a result, provide varied levels of compression. Using the task-based Legion programming model, a single-pass ID algorithm (SPID) for CFD applications is implemented. Performance studies, scalability, and the accuracy of the compression algorithm are presented for a benchmark analytical Taylor-Green vortex problem, as well as large-scale implementations of both low and high Reynolds number ( Re) compressible Taylor-Green vortices using a high-order Navier-Stokes solver. In the case of the analytical solution, the resulting compressed solution was rank-one, with error on the order of machine precision. For the low- Re vortex, compression factors between 1000 and 10,000 were achieved for errors in the range 10−2–10−3. Similar error values were seen for the high- Re vortex, this time with compression factors between 100 and 1000. Moreover, strong and weak scaling results demonstrate that introducing SPID to solvers leads to negligible increases in runtime.

On the mesh resolution of industrial LES based on the DNS of flow over the T106C turbine

A high-order Navier-Stokes solver based on the flux reconstruction (FR) or the correction procedure via reconstruction (CPR) formulation is employed to perform a direct numerical simulation (DNS) and large eddy simulations (LES) of a well-known benchmark problem – transitional flow over the low-pressure T106C turbine cascade. Hp-refinement studies are carried out to assess the resolution requirement. A 4th order (p3) simulation on the fine mesh is performed with a DNS resolution to establish a "converged" solution, including the mean pressure and skin-friction distributions, and the power spectral density in the wake. Then LES on the coarse and fine meshes with lower order schemes are conducted to assess the mesh and order dependence of the solution. In particular, we study the error in the transition location, the mean skin-friction distribution, and the mean lift and drag coefficients. These h- and p-refinement studies provide a much-needed guideline in h- and p- resolutions to achieve a certain level of accuracy for industrial LES applications.

Numerical Study of Shock/Boundary Layer Interaction of Chemically Reacting Flow in Shock Tube

In this paper, a high-order Navier-Stokes solver is developed for chemically reacting flow and is applied to investigate the unsteady, viscous interaction between shock wave and boundary layer in an air filled shock tube. The solver employs a high- resolution weighted essentially non-oscillatory (WENO) scheme to capture the complex flow pattern induced by shock/boundary- layer interaction, together with a point-implicit method to overcome the stiffness of chemical production term. The results show the influence of real gas effects and give insights into the mechanism of shock/boundary-layer interaction process.

On Flow-Acoustic Resonant Interactions in Transitional Airfoils

We discuss our recent experimental and preliminary numerical efforts examining resonant feedback mechanism of flow-acoustic interactions in airfoil transitional boundary layers. Experimentally recorded unsteady responses of loaded, transitional NACA0012 airfoil with tripped suction or pressure sides confirm the presence of shifted ladder-type tonal structures with dual velocity dependence in the acoustic signal previously reported in the literature. The installation of upstream grid generating low-intensity turbulence appears to eliminate the feedback mechanism leaving just a single velocity dependence for the dominant spectral components. Complementary numerical efforts employ a high-order Navier-Stokes solver implementing low-pass filtering of poorly resolved high-frequency solution content to retain numerical accuracy and stability over the range of transitional flow regimes. Within the scope of 2D analysis, the conducted numerical experiments particularly investigate the behavior of the boundary-layer statistical moments during the transitional flow regimes characterized by the presence of the acoustic feedback, and address sensitivity of the latter to the flow Reynolds number.

Computational study of detonation wave propagation in narrow channels

A numerical study of the propagation of regular detonation waves is conducted in the context of narrow channels undergoing strong wall confinement. To deal with shock waves, chemical reactions, heat and viscous stresses, a high-order Navier-Stokes solver based on Weighted Essentially Non-Oscillatory (WENO) scheme, coupled with the Strang splitting method, is used in the framework of multi-species reacting mixtures. Results show that the wall dissipative effects decrease the speed of the detonation wave compared to the Chapman-Jouguet (CJ) detonation velocity. In addition, the multidimensional results reveal that the development of the thermo-diffusive boundary layers behind the leading shock wave induces an expansion flow, which then determines the contour of the sonic envelope. From the Master Equation and the generalized CJ condition, which are derived and compared to the results of the current simulations, the main energy withdrawals are found to be related to the streamline divergence as well as to the growth of the boundary layer. Moreover, a fraction of the released energy is trapped in the vicinity of the wall and does not contribute to drive the shock front. The influence of the channel height is also investigated. It was found that the transverse instabilities are damped when the channel is scaled down, which results in an increase of the dissipative effects. Finally, the validity of the Fay model is discussed with regard to the channel height and the curvature of the detonation front.

Direct numerical simulation of dynamic three-fluid flow

Three-fluid flow is characterised by three different interfaces between fluids, which are among the most important issues in a three-fluid flow. The objective of this paper is to track the dynamic interfaces between fluids implicitly and then to computerise the flow hydrodynamics. We use the level-set method for the interface tracking and a high-order Navier-Stokes solver, called Cubic-Interpolated Pseudo-Particle (CIP) algorithm to solve the equation system. Firstly, a two-fluid situation is simulated to demonstrate the capability of the level-set method. Then, as an example, we simulate a drop which is covered by a layer of gas/vapour and is moving in a water pool. The dynamic processes, such as deformation of vapour layer and its detachment from the drop, are simulated.