The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Quantum ESPRESSO is an open-source distribution of computer codes for quantum-mechanical materials modeling, based on density-functional theory, pseudopotentials, and plane waves, and renowned for its performance on a wide range of hardware architectures, from laptops to massively parallel computers, as well as for the breadth of its applications. In this paper, we present a motivation and brief review of the ongoing effort to port Quantum ESPRESSO onto heterogeneous architectures based on hardware accelerators, which will overcome the energy constraints that are currently hindering the way toward exascale computing.

Quantum ESPRESSO toward the exascale.

Quantum ESPRESSO is an open-source distribution of computer codes for quantum-mechanical materials modeling, based on density-functional theory, pseudopotentials, and plane waves, and renowned for its performance on a wide range of hardware architectures, from laptops to massively parallel computers, as well as for the breadth of its applications. In this paper we present a motivation and brief review of the ongoing effort to port Quantum ESPRESSO onto heterogeneous architectures based on hardware accelerators, which will overcome the energy constraints that are currently hindering the way towards exascale computing.

We report the observation of superstructures, i.e., very large-scale and long living coherent structures in highly turbulent Rayleigh-Benard convection up to Rayleigh Ra=109. We perform direct numerical simulations in horizontally periodic domains with aspect ratios up to Γ=128. In the considered Ra number regime the thermal superstructures have a horizontal extend of six to seven times the height of the domain and their size is independent of Ra. Many laboratory experiments and numerical simulations have focused on small aspect ratio cells in order to achieve the highest possible Ra. However, here we show that for very high Ra integral quantities such as the Nusselt number and volume averaged Reynolds number only converge to the large aspect ratio limit around Γ≈4, while horizontally averaged statistics such as standard deviation and kurtosis converge around Γ≈8, the integral scale converges around Γ≈32, and the peak position of the temperature variance and turbulent kinetic energy spectra only converge around Γ≈64.

Turbulent thermal superstructures in Rayleigh-Bénard convection

Modern commodity processors such as GPUs may execute up to about a thousand of physical threads per chip to better utilize their numerous execution units and hide execution latencies. Understanding this novel capability, however, is hindered by the overall complexity of the hardware and complexity of typical workloads. In this dissertation, we suggest a better way to understand modern multithreaded performance by considering a family of synthetic workloads, which use the same key hardware capabilities – memory access, arithmetic operations, and multithreading – but are otherwise as simple as possible.One of our surprising findings is that prior performance models for GPUs fail on these workloads: they mispredict observed throughputs by factors of up to 1.7. We analyze these prior approaches, identify a number of common pitfalls, and discuss the related subtleties in understanding concurrency and Little’s Law. Also, we help to further our understanding by considering a few basic questions, such as on how different latencies compare with each other in terms of latency hiding, and how the number of threads needed to hide latency depends on basic parameters of executed code such as arithmetic intensity. Finally, we outline a performance modeling framework that is free from the found limitations.As a tangential development, we present a number of novel experimental studies, such as on how mean memory latency depends on memory throughput, how latencies of individual memory accesses are distributed around the mean, and how occupancy varies during execution.

/pdf/understanding-latency-hiding-on-gpus-40ive868jn.pdf

Understanding Latency Hiding on GPUs

AFiD-GPU: A versatile Navier–Stokes solver for wall-bounded turbulent flows on GPU clusters

CUDA Fortran for Scientists and Engineers shows how high-performance application developers can leverage the power of GPUs using Fortran, the familiar language of scientific computing and supercomputer performance benchmarking. The authors presume no prior parallel computing experience, and cover the basics along with best practices for efficient GPU computing using CUDA Fortran. To help you add CUDA Fortran to existing Fortran codes, the book explains how to understand the target GPU architecture, identify computationally intensive parts of the code, and modify the code to manage the data and parallelism and optimize performance. All of this is done in Fortran, without having to rewrite in another language. Each concept is illustrated with actual examples so you can immediately evaluate the performance of your code in comparison.Leverage the power of GPU computing with PGI's CUDA Fortran compilerGain insights from members of the CUDA Fortran language development teamIncludes multi-GPU programming in CUDA Fortran, covering both peer-to-peer and message passing interface (MPI) approachesIncludes full source code for all the examples and several case studies Download source code and slides from the book's companion website

CUDA Fortran for Scientists and Engineers: Best Practices for Efficient CUDA Fortran Programming

This chapter covers how to write code that utilizes multiple GPUs. Although there are many possible configurations between host processes and devices one can use in multi-GPU code, this chapter focuses on two configurations: (1) a single host process with multiple GPUs using CUDA’s peer-to-peer capabilities introduced in the 4.0 Toolkit, and (2) using MPI, where each MPI process uses a separate GPU. As an example of each of these approaches, we implement peer-to-peer and MPI multi-GPU versions of the transpose example used in the previous chapter.

Multi-GPU Programming

We describe the porting of PWscf (Plane-Wave Self Consistent Field), a key component of the Quantum ESPRESSO open-source suite of codes for materials modeling, to GPU systems using CUDA Fortran. Kernel loop directives (CUF kernels) have been extensively used in order to have a single source code for both CPU and GPU implementations. The results of the GPU version have been carefully validated and the performance of the code on several GPU systems (both x86 and POWER8 based) has been compared with traditional Intel multi-core (CPU only) systems. This current GPU version can reduce the time-to-solution by an average factor of 2–3 running two different input cases widely used as benchmarks on small and large high performance computing systems.

A Performance Study of Quantum ESPRESSO’s PWscf Code on Multi-core and GPU Systems

This chapter shows some applications of the Fast Fourier Transform and how to utilize the CUFFT library.

Gregory Ruetsch

Papers

AFiD-GPU: A versatile Navier–Stokes solver for wall-bounded turbulent flows on GPU clusters

CUDA Fortran for Scientists and Engineers: Best Practices for Efficient CUDA Fortran Programming

Multi-GPU Programming

A Performance Study of Quantum ESPRESSO’s PWscf Code on Multi-core and GPU Systems

Applications of Fast Fourier Transform