An efficient ghost-cell immersed boundary method (GCIBM) for simulating turbulent flows in complex geometries is presented. A boundary condition is enforced through a ghost cell method. The reconstruction procedure allows systematic development of numerical schemes for treating the immersed boundary while preserving the overall second-order accuracy of the base solver. Both Dirichlet and Neumann boundary conditions can be treated. The current ghost cell treatment is both suitable for staggered and non-staggered Cartesian grids. The accuracy of the current method is validated using flow past a circular cylinder and large eddy simulation of turbulent flow over a wavy surface. Numerical results are compared with experimental data and boundary-fitted grid results. The method is further extended to an existing ocean model (MITGCM) to simulate geophysical flow over a three-dimensional bump. The method is easily implemented as evidenced by our use of several existing codes.

A Ghost-Cell Immersed Boundary Method for Flow in Complex Geometry

A flux splitting scheme is proposed for the general nonequilibrium flow equations with an aim at removing numerical dissipation of Van-Leer-type flux-vector splittings on a contact discontinuity. The scheme obtained is also recognized as an improved Advection Upwind Splitting Method (AUSM) where a slight numerical overshoot immediately behind the shock is eliminated. The proposed scheme has favorable properties: high-resolution for contact discontinuities; conservation of enthalpy for steady flows; numerical efficiency; applicability to chemically reacting flows. In fact, for a single contact discontinuity, even if it is moving, this scheme gives the numerical flux of the exact solution of the Riemann problem. Various numerical experiments including that of a thermo-chemical nonequilibrium flow were performed, which indicate no oscillation and robustness of the scheme for shock/expansion waves. A cure for carbuncle phenomenon is discussed as well.

A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities(Proceedings of the 12th NAL Symposium on Aircraft Computational Aerodynamics)

Several new numerical methods for compressible shear-layer simulations

https://personal.egr.uri.edu/grilli/shi_etal_om_2012.pdf

A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation

Higher-order-accurate upwind schemes for solving the compressible Euler and Navier-Stokes equations

Stencil computation is one of the important kernels in scientific computations. However, sustained performance is limited owing to restriction on memory bandwidth, especially on multicore microprocessors and graphics processing units (GPUs) because of their small operational intensity. In this paper, we present a custom computing machine (CCM), called a scalable streaming-array (SSA), for high-performance stencil computations with multiple field-programmable gate arrays (FPGAs). We design SSA based on a domain-specific programmable concept, where CCMs are programmable with the minimum functionality required for an algorithm domain. We employ a deep pipelining approach over successive iterations to achieve linear scalability for multiple devices with a constant memory bandwidth. Prototype implementation using nine FPGAs demonstrates good agreement with a performance model, and achieves 260 and 236 GFlop/s for 2D and 3D Jacobi computation, which are 87.4 and 83.9 percent of the peak, respectively, with a memory bandwidth of only 2.0 GB/s. We also evaluate the performance of SSA for state-of-the-art FPGAs.

Multi-FPGA Accelerator for Scalable Stencil Computation with Constant Memory Bandwidth

This paper presents an FPGA-based flow solver based on the systolic architecture. We show that the fractional-step method employing central difference schemes can be expressed as a systolic algorithm, and therefore the systolic architecture is suitable for a dedicated processor to the flow solver. We have designed a 2D systolic array of cells, each of which has a micro-programmable data-path containing a MAC (multiplication and accumulation) unit and a local memory to store necessary data for computational fluid dynamics. With ALTERA Stratix II FPGA, we implemented 96(= 12 times 8) cells running at 60 MHz. Since the MAC unit has both an adder and a multiplier for single-precision floating-point numbers, the total peak performance is 11.5(= 96times60 MHztimes2) GFlops. We made a choice of 2D square driven cavity flow as a benchmark computation based on the fractional-step method. For this computation, the FPGA-based processor running only at 60 MHz achieved 7.14 and 6.41 times faster computations than Pentium4 processor at 3.2 GHz and Itanium2 at 1.4 GHz, respectively.

Systolic Architecture for Computational Fluid Dynamics on FPGAs

The purpose of the “International Wet Steam Modeling Project” is to review the ability of computational methods to predict condensing steam flows. The results of numerous wet-steam methods are comp...

https://journals.sagepub.com/doi/pdf/10.1177/0957650918758779

Results of the International Wet Steam Modeling Project

This paper presents an FPGA-based streaming computation for the lattice Boltzmann method (LBM) to simulate fluid flow with floating-point calculations. LBM is suitable for streaming computation because of its parallelism and regularity. We optimize the equations of LBM, and then formulate a streaming computation. To design an efficient data-path for throughput and hardware resource utilization, we introduce multiple cycle inputs and computing-unit sharing to the streaming data-path. The streaming accelerator implemented on a Virtex-4 FPGA with PCTExpress x8 interface achieves 2.93 and 2.46 times faster computation than a 3.4 GHz Pentium4 processor and a 2.2 GHz Opteron processor, respectively, for 2-dimensional time-dependent fluid dynamics problems.

Satoru Yamamoto

Papers

Higher-order-accurate upwind schemes for solving the compressible Euler and Navier-Stokes equations

Multi-FPGA Accelerator for Scalable Stencil Computation with Constant Memory Bandwidth

Systolic Architecture for Computational Fluid Dynamics on FPGAs

Results of the International Wet Steam Modeling Project

FPGA-based Streaming Computation for Lattice Boltzmann Method