A novel computational fluid dynamics framework for turbulent stream analysis – Google Analysis Weblog

Turbulence is ubiquitous in environmental and engineering fluid flows, and is encountered routinely in on a regular basis life. A greater understanding of those turbulent processes might present worthwhile insights throughout a wide range of analysis areas — bettering the prediction of cloud formation by atmospheric transport and the spreading of wildfires by turbulent vitality trade, understanding sedimentation of deposits in rivers, and bettering the effectivity of combustion in plane engines to cut back emissions, to call just a few. Nonetheless, regardless of its significance, our present understanding and our means to reliably predict such flows stays restricted. That is primarily attributed to the extremely chaotic nature and the big spatial and temporal scales these fluid flows occupy, starting from energetic, large-scale actions on the order of a number of meters on the high-end, the place vitality is injected into the fluid stream, all the best way right down to micrometers (μm) on the low-end, the place the turbulence is dissipated into warmth by viscous friction.

A robust instrument to know these turbulent flows is the direct numerical simulation (DNS), which supplies an in depth illustration of the unsteady three-dimensional flow-field with out making any approximations or simplifications. Extra particularly, this method makes use of a discrete grid with sufficiently small grid spacing to seize the underlying steady equations that govern the dynamics of the system (on this case, variable-density Navier-Stokes equations, which govern all fluid stream dynamics). When the grid spacing is sufficiently small, the discrete grid factors are sufficient to symbolize the true (steady) equations with out the lack of accuracy. Whereas that is enticing, such simulations require great computational assets with a purpose to seize the proper fluid-flow behaviors throughout such a variety of spatial scales.

The precise span in spatial decision to which direct numerical calculations have to be utilized is determined by the duty and is decided by the Reynolds number, which compares inertial to viscous forces. Sometimes, the Reynolds quantity can vary between 10² as much as 10⁷ (even bigger for atmospheric or interstellar issues). In 3D, the grid measurement for the decision required scales roughly with the Reynolds quantity to the facility of 4.5! Due to this sturdy scaling dependency, simulating such flows is usually restricted to stream regimes with reasonable Reynolds numbers, and sometimes requires entry to high-performance computing systems with thousands and thousands of CPU/GPU cores.

In “A TensorFlow simulation framework for scientific computing of fluid flows on tensor processing units”, we introduce a brand new simulation framework that allows the computation of fluid flows with TPUs. By leveraging newest advances on TensorFlow software program and TPU-hardware structure, this software program instrument permits detailed large-scale simulations of turbulent flows at unprecedented scale, pushing the boundaries of scientific discovery and turbulence evaluation. We show that this framework scales effectively to accommodate the dimensions of the issue or, alternatively, improved run instances, which is outstanding since most large-scale distributed computation frameworks exhibit lowered effectivity with scaling. The software program is offered as an open-source venture on GitHub.

Massive-scale scientific computation with accelerators

The software program solves variable-density Navier-Stokes equations on TPU architectures utilizing the TensorFlow framework. The single-instruction, multiple-data (SIMD) method is adopted for parallelization of the TPU solver implementation. The finite difference operators on a colocated structured mesh are forged as filters of the convolution operate of TensorFlow, leveraging TPU’s matrix multiply unit (MXU). The framework takes benefit of the low-latency high-bandwidth inter-chips interconnect (ICI) between the TPU accelerators. As well as, by leveraging the single-precision floating-point computations and extremely optimized executable by means of the accelerated linear algebra (XLA) compiler, it’s attainable to carry out large-scale simulations with glorious scaling on TPU {hardware} architectures.

This analysis effort demonstrates that the graph-based TensorFlow together with new varieties of ML particular goal {hardware}, can be utilized as a programming paradigm to resolve partial differential equations representing multiphysics flows. The latter is achieved by augmenting the Navier-Stokes equations with bodily fashions to account for chemical reactions, heat-transfer, and density modifications to allow, for instance, simulations of cloud formation and wildfires.

It’s value noting that this framework is the primary open-source computational fluid dynamics (CFD) framework for high-performance, large-scale simulations to completely leverage the cloud accelerators which have turn out to be widespread (and turn out to be a commodity) with the development of machine studying (ML) in recent times. Whereas our work focuses on utilizing TPU accelerators, the code will be simply adjusted for different accelerators, reminiscent of GPU clusters.

This framework demonstrates a approach to enormously scale back the price and turn-around time related to working large-scale scientific CFD simulations and permits even higher iteration pace in fields, reminiscent of local weather and climate analysis. Because the framework is applied utilizing TensorFlow, an ML language, it additionally permits the prepared integration with ML strategies and permits the exploration of ML approaches on CFD issues. With the overall accessibility of TPU and GPU {hardware}, this method lowers the barrier for researchers to contribute to our understanding of large-scale turbulent methods.

Framework validation and homogeneous isotropic turbulence

Past demonstrating the efficiency and the scaling capabilities, it is usually crucial to validate the correctness of this framework to make sure that when it’s used for CFD issues, we get cheap outcomes. For this goal, researchers sometimes use idealized benchmark issues throughout CFD solver improvement, lots of which we adopted in our work (extra particulars within the paper).

One such benchmark for turbulence evaluation is homogeneous isotropic turbulence (HIT), which is a canonical and nicely studied stream wherein the statistical properties, reminiscent of kinetic vitality, are invariant underneath translations and rotations of the coordinate axes. By pushing the decision to the bounds of the present state-of-the-art, we had been in a position to carry out direct numerical simulations with greater than eight billion levels of freedom — equal to a three-dimensional mesh with 2,048 grid factors alongside every of the three instructions. We used 512 TPU-v4 cores, distributing the computation of the grid factors alongside the x, y, and z axes to a distribution of [2,2,128] cores, respectively, optimized for the efficiency on TPU. The wall clock time per timestep was round 425 milliseconds and the stream was simulated for a complete of 400,000 timesteps. 50 TB information, which incorporates the rate and density fields, is saved for 400 timesteps (each 1,000th step). To our information, this is without doubt one of the largest turbulent stream simulations of its form carried out to this point.

Because of the advanced, chaotic nature of the turbulent stream subject, which extends throughout a number of magnitudes of decision, simulating the system in excessive decision is critical. As a result of we make use of a fine-resolution grid with eight billion factors, we’re in a position to precisely resolve the sector.

Contours of x-component of velocity alongside the z midplane. The excessive decision of the simulation is crucial to precisely symbolize the turbulent subject.

The turbulent kinetic vitality and dissipation charges are two statistical portions generally used to investigate a turbulent stream. The temporal decay of those properties in a turbulent subject with out further vitality injection is because of viscous dissipation and the decay asymptotes comply with the anticipated analytical power law. That is in settlement with the theoretical asymptotes and observations reported within the literature and thus, validates our framework.

Strong line: Temporal evolution of turbulent kinetic vitality (okay). Dashed line: Analytical energy legal guidelines for decaying homogeneous isotropic turbulence (n=1.3) (Ⲧl: eddy turnover time).

Strong line: Temporal evolution of dissipation charge (ε). Dashed line: Analytical energy legal guidelines for decaying homogeneous isotropic turbulence (n=1.3).

The vitality spectrum of a turbulent stream represents the vitality content material throughout wavenumber, the place the wavenumber okay is proportional to the inverse wavelength λ (i.e., okay ∝ 1/λ). Usually, the spectrum will be qualitatively divided into three ranges: supply vary, inertial vary and viscous dissipative vary (from left to proper on the wavenumber axis, beneath). The bottom wavenumbers within the supply vary correspond to the most important turbulent eddies, which have essentially the most vitality content material. These massive eddies switch vitality to turbulence within the intermediate wavenumbers (inertial vary), which is statistically isotropic (i.e., basically uniform in all instructions). The smallest eddies, comparable to the most important wavenumbers, are dissipated into thermal vitality by the viscosity of the fluid. By advantage of the effective grid having 2,048 factors in every of the three spatial instructions, we’re in a position to resolve the stream subject as much as the size scale at which viscous dissipation takes place. This direct numerical simulation method is essentially the most correct because it doesn’t require any closure mannequin to approximate the vitality cascade beneath the grid measurement.

Spectrum of turbulent kinetic vitality at totally different time cases. The spectrum is normalized by the instantaneous integral size (l) and the turbulent kinetic vitality (okay).

A brand new period for turbulent flows analysis

Extra just lately, we prolonged this framework to foretell wildfires and atmospheric flows, which is related for climate-risk evaluation. Aside from enabling high-fidelity simulations of advanced turbulent flows, this simulation framework additionally supplies capabilities for scientific machine learning (SciML) — for instance, downsampling from a effective to a rough grid (model reduction) or constructing fashions that run at decrease decision whereas nonetheless capturing the proper dynamic behaviors. It might additionally present avenues for additional scientific discovery, reminiscent of constructing ML-based fashions to higher parameterize microphysics of turbulent flows, together with bodily relationships between temperature, strain, vapor fraction, and so on., and will enhance upon numerous management duties, e.g., to cut back the vitality consumption of buildings or discover extra environment friendly propeller shapes. Whereas enticing, a principal bottleneck in SciML has been the provision of knowledge for coaching. To discover this, we’ve been working with teams at Stanford and Kaggle to make the info from our high-resolution HIT simulation accessible by means of a community-hosted web-platform, BLASTNet, to supply broad entry to high-fidelity information to the analysis neighborhood by way of a network-of-datasets method. We hope that the provision of those rising high-fidelity simulation instruments together with community-driven datasets will result in vital advances in numerous areas of fluid mechanics.

Acknowledgements

We wish to thank Qing Wang, Yi-Fan Chen, and John Anderson for consulting and recommendation, Tyler Russell and Carla Bromberg for program administration.