Session GB: Computational Fluid Dynamics III

A Superposition-Based Parallel Discrete Operator Splitting Technique for Incompressible Flows

Juxtaposition-based domain decomposition parallelization dominates in numeric computing. However, it suffers from complicated pre-processing and is restricted to field problems. In contrast, superposition-based parallelization shows great flexibility in partition of computational domains and follows the same numerical process as its serial counterpart, which makes code development and debugging much easier. In the other scenario, solving large scale indefinite systems continues to pose as a challenging issue. Many techniques exist but favors go to three categories of splitting methods, the continuous splitting, the semi-discrete splitting, and the discrete splitting. The underpinning idea of the proposed Discrete Operator Splitting (DOS) technique is to fully exploit the relation between the splitting and iterations. With the above two aspects combined, we present the superposition-based parallel discrete operator splitting finite element method and apply it to investigate incompressible Navier-Stokes flows. Finally, numerical examples are presented to demonstrate the success of the method.   

CFD Computations on Multi-GPU Configurations.

Programmable graphics processors have shown favorable potential for use in practical CFD simulations -- often delivering a speed-up factor between 3 to 5 times over conventional CPUs. In recent times, most PCs are supplied with the option of installing multiple GPUs on a single motherboard, thereby providing the option of a parallel GPU configuration in a shared-memory paradigm. We demonstrate our implementation of an unstructured CFD solver using a set up which is configured to run two GPUs in parallel, and discuss its performance details.   

Adaptive Flow Simulation of Turbulence in Subject-Specific Abdominal Aortic Aneurysm on Massively Parallel Computers

Flow within the healthy human vascular system is typically laminar but diseased conditions can alter the geometry sufficiently to produce transitional/turbulent flows in regions focal (and immediately downstream) of the diseased section. The mean unsteadiness (pulsatile or respiratory cycle) further complicates the situation making traditional turbulence simulation techniques (e.g., Reynolds-averaged Navier-Stokes simulations (RANSS)) suspect. At the other extreme, direct numerical simulation (DNS) while fully appropriate can lead to large computational expense, particularly when the simulations must be done quickly since they are intended to affect the outcome of a medical treatment (e.g., virtual surgical planning). To produce simulations in a clinically relevant time frame requires; 1) adaptive meshing technique that closely matches the desired local mesh resolution in all three directions to the highly anisotropic physical length scales in the flow, 2) efficient solution algorithms, and 3) excellent scaling on massively parallel computers. In this presentation we will demonstrate results for a subject-specific simulation of an abdominal aortic aneurysm using stabilized finite element method on anisotropically adapted meshes consisting of O($10^8$) elements over O($10^4$) processors.   

Jacobian-Free Newton-Krylov Discontinuous Galerkin (JFNK-DG) Method and Its Physics-Based Preconditioning for All-Speed Flows

The Discontinuous Galerkin (DG) method for compressible fluid flows is incorporated into the Jacobian-Free Newton-Krylov (JFNK) framework. Advantages of combining the DG with the JFNK are two-fold: $a)$ enabling \textit{robust and efficient high-order-accurate modeling of all-speed flows on unstructured grids}, opening the possibility for high-fidelity simulation of nuclear-power-industry-relevant flows; and $b)$ ability to \textit{tightly, robustly and high-order-accurately couple with other relevant physics} (neutronics, thermal-structural response of solids, etc.). In the present study, we focus on the physics-based preconditioning (PBP) of the Krylov method (GMRES), used as the linear solver in our implicit higher-order-accurate Runge-Kutta (ESDIRK) time discretization scheme; exploiting the compactness of the spatial discretization of the DG family. In particular, we utilize the \textit{Implicit Continuous-fluid Eulerian (ICE) method} and investigate its efficacy as the PBP within the JFNK-DG method. Using the eigenvalue analysis, it is found that the ICE collapses the complex components of the \underline {all eigenvalues} of the Jacobian matrix (associated with pressure waves) onto the real axis, and thereby enabling at least an order of magnitude faster simulations in nearly-incompressible/weakly-compressible regimes with a significant storage saving.   

Chimera grid simulations of falling spheres

Many applications involve modeling a system with moving objects larger than the grid, such as air pollution, combustion systems, accident simulations, chemical and agricultural processes. The chimera grid approach is an efficient approach to solve such problems. Simulations of one sphere falling under the influence of gravity and suction through an orifice will be presented. Additionally, we will demonstrate collisions between two moving spheres. In this simulation the setup is the same as in the one sphere case, but two spheres are placed side by side. Both are released to be acted upon by gravity, the suction, and each other.   

Discrete kinetic energy conservation for variable-density flows on staggered grids

It is now conventional wisdom that ``kinetic-energy (KE)-conserving'' numerical methods are to be preferred for use in large-eddy simulation due to accuracy and stability considerations. For constant-density flows, KE-conserving schemes generally require central differencing and it is common practice to simply apply the same central differencing schemes to variable-density flows without the same rigorous stability guarantees. The theory for semi-discrete KE conservation for constant-density flows is worked out by [Morinishi et al., \textit{J. Comp. Phys}., 1998]. The requirement of centered time advancement is shown by [Ham et al., \textit{J. Comp. Phys}., 2002]. As a work-in-progress toward development of a fully conservative scheme for variable-density flows, we extend the Morinishi/Ham analysis for Cartesian staggered grids to include variable density and show that KE conservation requires discrete conservation of mass within each of the staggered momentum cells. This may allow the design of fully conservative schemes for variable-density flows.   

Parallel Simulations of Turbulent Channel Flow Using Regular and Entropic Lattice Boltzmann Schemes

Lattice Boltzmann methods (LBM) have proven to be reliable tools for the simulation of a variety of complex flows. One of their advantages is that they lend themselves to efficient implementations on parallel computers. In this talk we demonstrate this advantage by presenting results from a parallel direct numerical simulation of a fully developed, incompressible, pressure driven turbulent channel flow. The results are compared to results obtained using a standard Chebyshev pseudo-spectral method. In the second part of the talk, the entropic version of the Lattice Boltzmann method (ELBM) is presented. It renders LBM non-linearly stable and hence one could in principle use fewer grid points without the risk of numerical instability. We address the question of accuracy when under-resolved simulations of turbulent channel flow are carried out using ELBM.   

A Novel Neural-Multigrid Strategy to Solve Compressible Euler Equation in Nozzle Using Finite Volume Method

In this research, a Neural-Multigrid technique is developed for solving Euler equation in nozzle using an implicit finite volume method. In this regard, the nested iteration strategy is used to achieve more accurate numerical guess during the iterations. As restriction and interpolation operators for transferring of data between coarse and fine grids only a Supervised Multilayer Perceptron Neural Network (MLPR) with one hidden layer is used. During the iterations a pre-conditioning switching matrix is employed as a technique to boost up the method. For iteration on error, a sparse real system solving strategy by Gaussian elimination is employed which uses Markowitz strategy and LU factorization, the result of simulation shows the robustness of the method.   

Simulation of 2D and 3Dcavity flow using the Lattice Boltzmann Method

The lid-driven cavity flow is a well-known benchmark problem for fluid simulations. Due to the simplicity of the cavity geometry, numerical simulation is relatively easy and straightforward; in addition, it retains a rich flow physics manifested by the vortex structures in the center and corner regions varying with the Reynolds number (Re). Therefore, it has been studied extensively by different simulation approaches. But still there are some aspects which are not agreed upon and need further investigation. All simulations are conducted by using the Lattice Boltzmann Method in fine grid systems and with parallel algorithm. First, some detailed results are presented and compared with classic solutions found in literatures for code validation. Then the transition process from laminar to turbulent flow in 2D and 3D situations are conducted by increasing the Reynolds number; detailed results for time-velocity histories, and relative Fourier power spectra, phase diagram are given. Some accuracy estimation will be also included.