scholarly journals CFD Julia: A Learning Module Structuring an Introductory Course on Computational Fluid Dynamics

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 159 ◽  
Author(s):  
Suraj Pawar ◽  
Omer San
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Finite Difference ◽  
Stokes Equations ◽  
Iterative Solvers ◽  
Navier Stokes ◽  
Finite Difference Schemes ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Computational Performance

CFD Julia is a programming module developed for senior undergraduate or graduate-level coursework which teaches the foundations of computational fluid dynamics (CFD). The module comprises several programs written in general-purpose programming language Julia designed for high-performance numerical analysis and computational science. The paper explains various concepts related to spatial and temporal discretization, explicit and implicit numerical schemes, multi-step numerical schemes, higher-order shock-capturing numerical methods, and iterative solvers in CFD. These concepts are illustrated using the linear convection equation, the inviscid Burgers equation, and the two-dimensional Poisson equation. The paper covers finite difference implementation for equations in both conservative and non-conservative form. The paper also includes the development of one-dimensional solver for Euler equations and demonstrate it for the Sod shock tube problem. We show the application of finite difference schemes for developing two-dimensional incompressible Navier-Stokes solvers with different boundary conditions applied to the lid-driven cavity and vortex-merger problems. At the end of this paper, we develop hybrid Arakawa-spectral solver and pseudo-spectral solver for two-dimensional incompressible Navier-Stokes equations. Additionally, we compare the computational performance of these minimalist fashion Navier-Stokes solvers written in Julia and Python.

Numerical analysis of textured piston compression ring conjunction using two-dimensional-computational fluid dynamics and Reynolds methods

2018 ◽  
Vol 232 (11) ◽  
pp. 1467-1485 ◽  
Author(s):  
Chengwei Wen ◽  
Xianghui Meng ◽  
Wenxiang Li
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Compression Ring ◽  
Dynamics Method

The Reynolds equation, in which some items have been omitted, is a simplified form of the Navier–Stokes equations. When surface texturing exists, it may unreasonably reveal the tribological effects in some cases. In this paper, both the two-dimensional computational fluid dynamics method, which is based on the Navier–Stokes equations, and the corresponding one-dimensional Reynolds method are adopted to analyze the performance of the textured piston compression ring conjunction. To conduct a comparison between these two methods, the modified Elrod algorithm for Jakobsson–Floberg–Olsson cavitation model is chosen to solve the Reynolds equation. The results show that the Reynolds method is somewhat different from the computational fluid dynamics method in the minimum oil film thickness, pressure distribution, and cavitation at given operating conditions. Moreover, for a low ratio of texture depth to length, the Reynolds equation is still suitable to predict the overall effects of the designed groove textures. The simulation results also reveal that it is not always beneficial for the tribological performance and sometimes may increase the total friction force when the ring is textured.

Development of SIMPLE-Like Algorithms for Incompressible Navier-Stokes Equations in Liquid Processing of Materials

2012 ◽  
Vol 184-185 ◽  
pp. 944-948 ◽  
Author(s):  
Hai Jun Gong ◽  
Yang Liu ◽  
Xue Yi Fan ◽  
Da Ming Xu
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Stokes Equations ◽  
Simple Algorithm ◽  
Navier Stokes ◽  
Incompressible Fluid Flow ◽  
Numerical Accuracy ◽  
Simple Scheme ◽  
Navier Stokes Equations ◽  
Computational Fluid Dynamics Cfd

For a clear and comprehensive opinion on segregated SIMPLE algorithm in the area of computational fluid dynamics (CFD) during liquid processing of materials, the most significant developments on the SIMPLE algorithm and its variants are briefly reviewed. Subsequently, some important advances during last 30 years serving as increasing numerical accuracy, enhancing robustness and improving efficiency for Navier–Stokes (N-S) equations of incompressible fluid flow are summarized. And then a so-called Direct-SIMPLE scheme proposed by the authors of present paper introduced, which is different from SIMPLE-like schemes, no iterative computations are needed to achieve the final pressure and velocity corrections. Based on the facts cited in present paper, it conclude that the SIMPLE algorithm and its variants will continue to evolve aimed at convergence and accuracy of solution by improving and combining various methods with different grid techniques, and all the algorithms mentioned above will enjoy widespread use in the future.

A Survey of General Purpose Computation of GPU for Computational Fluid Dynamics

2013 ◽  
Vol 753-755 ◽  
pp. 2731-2735
Author(s):  
Wei Cao ◽  
Zheng Hua Wang ◽  
Chuan Fu Xu
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
High Performance ◽  
Stokes Equations ◽  
Gpu Computing ◽  
Graphics Processing Unit ◽  
General Purpose ◽  
Navier Stokes ◽  
Processing Unit ◽  
Gpgpu Computing

The graphics processing unit (GPU) has evolved from configurable graphics processor to a powerful engine for high performance computer. In this paper, we describe the graphics pipeline of GPU, and introduce the history and evolution of GPU architecture. We also provide a summary of software environments used on GPU, from graphics APIs to non-graphics APIs. At last, we present the GPU computing in computational fluid dynamics applications, including the GPGPU computing for Navier-Stokes equations methods and the GPGPU computing for Lattice Boltzmann method.

scholarly journals A Massively Parallel Hybrid Finite Volume/Finite Element Scheme for Computational Fluid Dynamics

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2316
Author(s):  
Laura Río-Martín ◽  
Saray Busto ◽  
Michael Dumbser
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Finite Element ◽  
Mach Number ◽  
Finite Volume ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Massively Parallel ◽  
Navier Stokes ◽  
Navier Stokes Equations

In this paper, we propose a novel family of semi-implicit hybrid finite volume/finite element schemes for computational fluid dynamics (CFD), in particular for the approximate solution of the incompressible and compressible Navier-Stokes equations, as well as for the shallow water equations on staggered unstructured meshes in two and three space dimensions. The key features of the method are the use of an edge-based/face-based staggered dual mesh for the discretization of the nonlinear convective terms at the aid of explicit high resolution Godunov-type finite volume schemes, while pressure terms are discretized implicitly using classical continuous Lagrange finite elements on the primal simplex mesh. The resulting pressure system is symmetric positive definite and can thus be very efficiently solved at the aid of classical Krylov subspace methods, such as a matrix-free conjugate gradient method. For the compressible Navier-Stokes equations, the schemes are by construction asymptotic preserving in the low Mach number limit of the equations, hence a consistent hybrid FV/FE method for the incompressible equations is retrieved. All parts of the algorithm can be efficiently parallelized, i.e., the explicit finite volume step as well as the matrix-vector product in the implicit pressure solver. Concerning parallel implementation, we employ the Message-Passing Interface (MPI) standard in combination with spatial domain decomposition based on the free software package METIS. To show the versatility of the proposed schemes, we present a wide range of applications, starting from environmental and geophysical flows, such as dambreak problems and natural convection, over direct numerical simulations of turbulent incompressible flows to high Mach number compressible flows with shock waves. An excellent agreement with exact analytical, numerical or experimental reference solutions is achieved in all cases. Most of the simulations are run with millions of degrees of freedom on thousands of CPU cores. We show strong scaling results for the hybrid FV/FE scheme applied to the 3D incompressible Navier-Stokes equations, using millions of degrees of freedom and up to 4096 CPU cores. The largest simulation shown in this paper is the well-known 3D Taylor-Green vortex benchmark run on 671 million tetrahedral elements on 32,768 CPU cores, showing clearly the suitability of the presented algorithm for the solution of large CFD problems on modern massively parallel distributed memory supercomputers.

Computational Fluid Dynamics of Four-Quadrant Marine-Propulsor Flow

1999 ◽  
Vol 43 (04) ◽  
pp. 218-228
Author(s):  
Bin Chen ◽  
Frederick Stern
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Verification And Validation ◽  
Navier Stokes ◽  
Ring Vortex ◽  
Reynolds Averaged Navier Stokes ◽  
Four Quadrant ◽  
Marine Propulsor

Computational fluid dynamics results are presented of four-quadrant flow for marine-propulsor P4381. The solution method is unsteady three-dimensional incompressible Reynolds-averaged Navier-Stokes equations in generalized coordinates with the Baldwin-Lomax turbulence model. The method was used previously for the design condition for marine-propulsor P4119, including detailed verification and validation. Only limited verification is performed for P4381. The validation is limited by the availability of four-quadrant performance data and ring vortex visualizations for the crashback conditions. The predicted performance shows close agreement with the data for the forward and backing conditions, whereas for the crashahead and crashback conditions the agreement is only qualitative and requires an ad hoc cavitation correction. Also, the predicted ring vortices for the crashback conditions are in qualitative agreement with the data. Extensive calculations enable detailed description of flow characteristics over a broad range of propulsor four-quadrant operations, including surface pressure and streamlines, velocity distributions, boundary layer and wake, separation, and tip and ring vortices. The overall results suggest promise for Reynolds-averaged Navier-Stokes methods for simulating marine-propulsor flow, including offdesign. However, important outstanding issues include additional verification and validation, time-accurate solutions, and resolution and turbulence modeling for separation and tip and ring vortices.

scholarly journals Direct control of the small-scale energy balance in two-dimensional fluid dynamics

2015 ◽  
Vol 782 ◽  
pp. 240-259 ◽  
Author(s):  
Jason Frank ◽  
Benedict Leimkuhler ◽  
Keith W. Myerscough
Keyword(s):  
Fluid Dynamics ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
High Fidelity Simulation ◽  
Two Dimensional ◽  
Feedback Controls ◽  
Navier Stokes Equations ◽  
Direct Modification ◽  
Pseudo Spectral

We explore the direct modification of the pseudo-spectral truncation of two-dimensional, incompressible fluid dynamics to maintain a prescribed kinetic energy spectrum. The method provides a means of simulating fluid states with defined spectral properties, for the purpose of matching simulation statistics to given information, arising from observations, theoretical prediction or high-fidelity simulation. In the scheme outlined here, Nosé–Hoover thermostats, commonly used in molecular dynamics, are introduced as feedback controls applied to energy shells of the Fourier-discretized Navier–Stokes equations. As we demonstrate in numerical experiments, the dynamical properties (quantified using autocorrelation functions) are only modestly perturbed by our device, while ensemble dispersion is significantly enhanced compared with simulations of a corresponding truncation incorporating hyperviscosity.

Steady two-dimensional flow through a row of normal flat plates

1990 ◽  
Vol 210 ◽  
pp. 281-302 ◽  
Author(s):  
D. B. Ingham ◽  
T. Tang ◽  
B. R. Morton
Keyword(s):  
Finite Difference ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Corner Singularities ◽  
Flat Plates ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
Good Agreement

A numerical and experimental study is described for the two-dimensional steady flow through a uniform cascade of normal flat plates. The Navier–Stokes equations are written in terms of the stream function and vorticity and are solved using a second-order-accurate finite-difference scheme which is based on a modified procedure to preserve accuracy and iterative convergence at higher Reynolds numbers. The upstream and downstream boundary conditions are discussed and an asymptotic solution is employed both upstream and downstream. A frequently used method for dealing with corner singularities is shown to be inaccurate and a method for overcoming this problem is described. Numerical solutions have been obtained for blockage ratio of 50 % and Reynolds numbers in the range 0 [les ]R[les ] 500 and results for both the lengths of attached eddies and the drag coefficients are presented. The calculations indicate that the eddy length increases linearly withR, at least up toR= 500, and that the multiplicative constant is in very good agreement with the theoretical prediction of Smith (1985a), who considered a related problem. In the case ofR= 0 the Navier–Stokes equations are solved using the finite-difference scheme and a modification of the boundary-element method which treats the corner singularities. The solutions obtained by the two methods are compared and the results are shown to be in good agreement. An experimental investigation has been performed at small and moderate values of the Reynolds numbers and there is excellent agreement with the numerical results both for flow streamlines and eddy lengths.

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