Thứ Bảy, 13 tháng 6, 2020

"3 weeks" series - OpenFOAM


"3 weeks" series

Jump to navigation Jump to search In this series you will have the possibility to get a more detailed understanding of the basics of OpenFOAM. You will be able to complete it in about three weeks. It is understandable, that you are exited. Everybody is, but please do not work on the weekends. Breaks are important for the learning process. This is the reason, why the tutorials are divided into fifteen days (see figure below). Do not skip the weekends! Some time without OpenFOAM is also important. You can start by clicking Day 1 below.
Go back to Tutorials.

Installing OpenFOAM

In order to be able to complete the tutorials, you will have to install OpenFOAM. There are multiple ways to do this. First, follow the official guideline here.
Alternatively, you can follow the video tutorial of Jozsef Nagy or the written tutorial of Joel Guerrero.
If you prefer Windows 10, you can find a tutorial on installing OpenFOAM in Windows 10 here.

General overview of the "3 weeks" tutorial series

3-weeks-series
Day 1 Day 2 Day 3 Day 4 Day 5
install - first steps steps - visualization introductory course discretization theory - fun simulations - tips
Day 6 Day 7 Day 8 Day 9 Day 10
geometry and meshing turbulence 1 turbulence 2 multiphase parallelization
Day 11 Day 12 Day 13 Day 14 Day 15
programming 1 programming 2 programming 3 programming 4 programming 5

Day 1

On Day 1 you will start to get familiar with OpenFOAM. Just follow the instructions step by step and familiarize yourself with the concept of OpenFOAM, Linux, the terminal and working with dictionaries.
  • basic workflow in OpenFOAM
  • getting used to the terminal
  • meshing with the OpenFOAM internal meshing utility blockMesh
  • running simulations
  • first steps with postprocessing in Paraview

Day 2

On Day 2 you will continue with your first steps. You will get an even deeper understanding and learn the work flow of OpenFOAM with a special focus on visualization of results.
  • more detailed understanding of the work flow
  • further short and fun simulations
  • grid convergence
  • transport equations
  • detailed scientific visualization of results

Day 3

On Day 3 you will digest all the information from the previous days by listening to a talk on the basics of OpenFOAM.

Day 4

On Day 4 you will understand the theory behind OpenFOAM by taking a detailed look at the discretization of the equations and the numerical settings. We will cover a big theoretical area about
  • gradient scheme
  • gradient limiter
  • convection discretization
  • face interpolation
  • diffusion discretization
  • influence of discretization on the simulation results
  • CFL number
  • linear solvers
  • solution methods

Day 5

Day 5 is there to round off the week with some fun simulations. Also we give you links to some interesting documents, which can help you solve your problems in OpenFOAM in the future.

Day 6

Day 6 is all about meshing. In order to be able to run simulation for real life problems, you have to understand how to create an arbitrary high quality mesh and which alternatives you have in OpenFOAM. For this you will learn about
  • geometry creation
  • mesh generation

Day 7

On Day 7 we will talk about turbulence modeling, as this is one of the most important aspects in a CFD simulation. It is important to understand the models as well as the difference between them ion order to choose the correct one for a given problem. Here we will cover the following topics:
  • steady-state turbulence modeling
  • transient turbulence modeling
  • Reynolds-Averaged Navier-Stokes equations
  • Large Eddy Simulations
  • initial and boundary conditions
  • case setup

Day 8

On day 8 we continue our investigation of turbulence modeling by doing extensive parameter studies to understand the idea behind turbulence modeling, the difference between models and the actual application. After this day you will be able to choose the correct model for your own problem.

Day 9

On Day 9 we will start another important topic in CFD, multiphase modeling. It is important to understand the additional physics involved to correctly set up the simulation case and to run the simulation. We will take a look at the available models and focus on the Volume-Of-Fluid Method and run several simulations to fully understand the theory and to gain experience in the simulations.

Day 10

On Day 10 we will take a look at the possibility to parallelize simulations in OpenFOAM. This is important, as high-quality simulation setups tend to be computationally very intensive. In order to reduce computation time, you will learn about
  • the idea of parallelization
  • domain decomposition
  • steps of parallelization
  • postprocessing parallel results

Day 11

On Day 11 we will take a look at programming. Today is all about the initial steps. By now you should be able to run simulations of real life problems with OpenFOAM. In some cases models might not be implemented in the source code. OpenFOAM offers through an open source code the possibility to add models to the existing code. This might be a challenging task, but with the following tutorials, you will get a basic understanding of the work flow.

Day 12

On day 12 we will further explore the programming possibilities OpenFOAM offers to extend the source code according to our needs. First we start with a video of Professor Jasak on programming. Can you follow the other two tutorials after that?

Day 13

(https://wiki.openfoam.com)

Although you already programmed applications the days before, on Day 13 we take a look at the basics of C++ and start with simple examples, so you can view them from a C++ perspective.

Day 14

Today we continue with programming. There is only one tutorial, but this tutorial consist of multiple examples and explains a lot.

Day 15

On Day 15 we finalize our 3-weeks-series by doing a fun programming simulation and going through a couple of pages of pdf.

End of the 3-weeks-series

We reached the end of Day 15 and with that the end of the 3-weeks-series. Now, now... Let's not get emotional here. Let's think about all the great challenges and successes in your CFD career with OpenFOAM and look forward to the future.
Also you can take a look at the collection by topic, where you can find further tutorials in different topics.
With this in mind... cheers!

Thứ Tư, 10 tháng 6, 2020

Numerical Mathematics and Computing



Preface


  1. Introduction   1.1 Preliminary Remarks
    1.2 Review of Taylor Series
  2. Floating-Point Representation and Errors 2.1 Floating-Point Representation
    2.2 Loss of Significance
  3. Locating Roots of Equations 3.1 Bisection Method
    3.2 Newton's Method
    3.3 Secant Method
  4. Interpolation and Numerical Differentiation 4.1 Polynomial Interpolation
    4.2 Errors in Polynomial Interpolation
    4.3 Estimating Derivatives and Richardson Extrapolation
  5. Numerical Integration 5.1 Lower and Upper Sums
    5.2 Trapezoid Rule
    5.3 Romberg Algorithm
  6. Additional Topics on Numerical Integration 6.1 Simpson's Rule and Adaptive Simpson's Rule
    6.2 Gaussian Quadrature Formulas
  7. Systems of Linear Equations 7.1 Naive Gaussian Elimination
    7.2 Gaussian Elimination with Scaled Partial Pivoting
    7.3 Tridiagonal and Banded Systems
  8. Additional Topics on Systems of Linear Equations 8.1 Matrix Factorizations
    8.2 Iterative Solution of Linear Systems
    8.3 Eigenvalues and Eigenvectors
    8.4 Power Methods
  9. Approximation by Spline Functions 9.1 First-Degree and Second-Degree Splines
    9.2 Natural Cubic Splines
    9.3 B Splines: Interpolation and Approximation
  10. Ordinary Differential Equations 10.1 Taylor Series Methods
    10.2 Runge-Kutta Methods
    10.3 Stability, Adaptive Runge-Kutta Methods, and Multistep Methods
  11. Systems of Ordinary Differential Equations 11.1 Methods for First-Order Systems
    11.2 Higher-Order Equations and Systems
    11.3 Adams-Bashforth-Moulton Methods
  12. Smoothing of Data and the Method of Least Squares 12.1 Method of Least Squares
    12.2 Orthogonal Systems and Chebyshev Polynomials
    12.3 Other Examples of the Least Squares Principle
  13. Monte Carlo Methods and Simulation 13.1 Random Numbers
    13.2 Estimation of Areas and Volumes by Monte Carlo Techniques
    13.3 Simulation
  14. Boundary Value Problems for Ordinary Differential Equations 14.1 Shooting Method
    14.2 A Discretization Method
  15. Partial Differential Equations 15.0 Some Partial Differential Equations from Applied Problems
    15.1 Parabolic Problems
    15.2 Hyperbolic Problems
    15.3 Elliptic Problems
  16. Minimization of Multivariate Functions 16.1 One-Variable Case
    16.2 Multivariate Case
  17. Linear Programming 17.1 Standard Forms and Duality
    17.2 Simplex Method
    17.3 Approximate Solution of Inconsistent Linear Systems

Appendix A: Advice on Good Programming Practices

Appendix B: Representation of Numbers in Different Bases

Appendix C: Additional Details on IEEE Floating-Point Arithmetic

Appendix D: Linear Algebra Concepts and Notation

Answers for Selected Problems

Bibliography

Index  


C3   C6   C7

Thứ Ba, 9 tháng 6, 2020

Relationships between undrained shear strength su and liquidity index IL and water content ratio WCR


 Table 1 Relationships between undrained shear strength su and liquidity index IL and water content ratio WCR

Table 2 Undrained shear strength at liquid and plastic limits of soils (sLL, sPL) and its strength ratio (Rs). Figures in parenthesis are average or recommended values

 

Reference:

Shimobe (2020) Relationships between undrained shear strength, liquidity index, and water content.pdf

Bài giảng Excel hay


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(Data Science & Big Data Vietnam)