CFD Python: the 12 steps to Navier-Stokes equations

Barba, Lorena A.; Forsyth, Gilbert

doi:10.21105/jose.00021

Cited by 29 publications

(27 citation statements)

References 3 publications

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“…14. The solution of the convection equation is displayed in Fig. 15 that shows the evolution of the field u, and the solution is consistent with the expected result produced by Barba and Forsyth (2018).…”

Section: Convectionsupporting

confidence: 78%

“…Devito aims to combine the performance benefits of dedicated stencil frameworks (Bondhugula et al, 2008;Tang et al, 2011;Henretty et al, 2013;Yount, 2015) with the expressiveness of symbolic PDE-solving DSLs (Logg et al, 2012;Rathgeber et al, 2015) through automated code generation and optimization from high-level symbolic expressions of the mathematics. Thus, the primary design objectives of the Devito DSL are to allow users to define explicit finitedifference operators for (time-dependent) PDEs in a concise symbolic manner and provide an API that is flexible enough to fully support realistic scientific use cases.…”

Section: Code Generation -An Overviewmentioning

confidence: 99%

“…The three examples we describe here are the convection equation, the Burgers' equation, and the Poisson equation. These examples are adapted from Barba and Forsyth (2018), and the example repository contains both the original Python implementation with NumPy and the implementation with Devito for comparison.…”

Section: Computational Fluid Dynamicsmentioning

confidence: 99%

“…Two prominent contemporary projects based on the finite-element method (FEM), FEniCS (Logg et al, 2012) and Firedrake (Rathgeber et al, 2015), both implement a common DSL, UFL (Alnaes et al, 2014), that allows for the expression of variational problems in weak form. Multiple DSLs to express stencillike algorithms have also emerged over time (Henretty et al, 2013;Zhang and Mueller, 2012;Christen et al, 2011;Unat et al, 2011;Köster et al, 2014;Membarth et al, 2012;Osuna et al, 2014;Tang et al, 2011;Bondhugula et al, 2008;Yount, 2015). Other stencil DSLs have been developed with the objective of solving PDEs using finite differences (Hawick and Playne, 2013;Arbona et al, 2017;Jacobs et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

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Devito (v3.1.0): an embedded domain-specific language for finite differences and geophysical exploration

et al. 2019

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Abstract. We introduce Devito, a new domain-specific language for implementing high-performance finite-difference partial differential equation solvers. The motivating application is exploration seismology for which methods such as full-waveform inversion and reverse-time migration are used to invert terabytes of seismic data to create images of the Earth's subsurface. Even using modern supercomputers, it can take weeks to process a single seismic survey and create a useful subsurface image. The computational cost is dominated by the numerical solution of wave equations and their corresponding adjoints. Therefore, a great deal of effort is invested in aggressively optimizing the performance of these wave-equation propagators for different computer architectures. Additionally, the actual set of partial differential equations being solved and their numerical discretization is under constant innovation as increasingly realistic representations of the physics are developed, further ratcheting up the cost of practical solvers. By embedding a domain-specific language within Python and making heavy use of SymPy, a symbolic mathematics library, we make it possible to develop finite-difference simulators quickly using a syntax that strongly resembles the mathematics. The Devito compiler reads this code and applies a wide range of analysis to generate highly optimized and parallel code. This approach can reduce the development time of a verified and optimized solver from months to days.

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Section: Convectionsupporting

confidence: 78%

Section: Code Generation -An Overviewmentioning

confidence: 99%

Section: Computational Fluid Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Devito (v3.1.0): an embedded domain-specific language for finite differences and geophysical exploration

et al. 2019

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“…I started using Jupyter for teaching in 2013 (when it still had not arXiv:2001.00228v1 [cs.CY] 16 Dec 2019 adopted this name). Based on a practical module used in the classroom in my Computational Fluid Dynamics (CFD) course (taught from 2010 to 2013 at Boston University), my first series of fully narrated notebooks is "CFD Python: the 12 steps to Navier-Stokes equations" [6]. Based on the experience creating and using the CFD Python learning module, and following a similar approach in later courses, we adopted this basic design pattern for developing lessons using computable content: 1) Break it down into small steps 2) Chunk small steps into bigger steps 3) Add narrative and connect 4) Link out to documentation 5) Interleave easy exercises 6) Spice with challenge questions/tasks 7) Publish openly online…”

Section: Key Concepts and Design Principlesmentioning

confidence: 99%

Engineers Code: Reusable Open Learning Modules for Engineering Computations

Barba

2020

Comput. Sci. Eng.

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Undergraduate programs in science and engineering include at least one course in basic programming, but seldom presented in a contextualized format, where computing is a tool for thinking and learning in the discipline. We have created a series of learning modules to embed computing in engineering education, and share this content under permissive public licenses. The modules are created as a set of lessons using Jupyter notebooks, and complemented by online courses in the Open edX platform, using new integrations we developed. Learning sequences in the online course pull content dynamically from public Jupyter notebooks and assessments are auto-graded on-the-fly, using our Jupyter Viewer and Jupyter Grader third-party extensions for Open edX (XBlocks). The learning content is modularized and designed for reuse in various formats. In one of these formats-short but intense workshops-our university library is leveraging the curriculum to offer extra-curricular training for all, at high demands.

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Study on the use of a combination of IPython Notebook and an industry‐standard package in educating a CFD course

Seddighi

Allanson

Rothwell

et al. 2020

Comp Applic In Engineering

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It is common that industry‐standard packages are used in teaching professional engineering courses in final‐year undergraduate and postgraduate levels. To improve the competency of students in using such professional packages, it is important that students develop a good understanding of theoretical/fundamental concepts used on the packages. However, it is always a challenge to teach theoretical/fundamental concepts in the computational‐related courses. The teaching of such subjects can be improved by the use of advanced open‐source web applications. The present research proposes an approach based upon the combination of Jupyter Notebook and an industry‐standard package to teach an applied, computationally related course. We investigate the use of backward design and a novel tool called IPython (Jupyter) Notebook to redesign a postgraduate Computational Fluid Dynamics (CFD) course. IPython Notebook is used to design a series of integrated lecture slides and tutorial tasks, and also one of the assignments for the blended‐learning‐based, semester‐run, CFD course. The tool allows the implementation of backward curriculum design and a learn‐by‐doing approach in redesigning the course. The materials produced were used on the first part of the course which contributed 40% towards the course's final mark and delivered the fundamental concepts of CFD over the first half of the semester. The remaining 60% of the mark was based on a final project from the materials taught on using an industry‐standard CFD package in solving complex CFD problems during the second half of the semester. It was shown that the Ipython environment is a very useful tool which provides learning‐by‐doing practices allowing students to have a coherent integrated lecture, tutorial, and assignment material in a highly interactive way. It improved (a) students' engagement in teaching complex theoretical concepts, (b) students satisfaction of the course and (c) students performance in working with the industry‐standard package over the second half of the semester.

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CFD Python: the 12 steps to Navier-Stokes equations

Abstract: License Authors of papers retain copyright and release the work under a Creative Commons Attribution 4.0 International License (CC-BY).

Cited by 29 publications

References 3 publications

Devito (v3.1.0): an embedded domain-specific language for finite differences and geophysical exploration

Devito (v3.1.0): an embedded domain-specific language for finite differences and geophysical exploration

Engineers Code: Reusable Open Learning Modules for Engineering Computations

Study on the use of a combination of IPython Notebook and an industry‐standard package in educating a CFD course

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