- Видео 22
- Просмотров 9 403
Milovan Peric
Германия
Добавлен 28 апр 2024
19. Examples of solutions of Navier-Stokes equations for steady flows using SIMPLE and IFSM methods
Implicit fractional step method (IFSM) and SIMPLE algorithm described in lectures 17 and 18 were applied to two two-dimensional test cases which are widely used for testing solution methods for the Navier-Stokes equations: lid-driven and buoyancy-driven flow in a square cavity. The aim of this lecture is to show how different choices affect the efficiency of the iterative solution process and the accuracy of the obtained solutions. Six systematically refined uniform grids and five non-uniform grids are used to test the grid-dependence and convergence rate toward grid-independent solution. SIMPLE algorithm is tested with both staggered and collocated arrangements of variables on the same g...
Просмотров: 97
Видео
18. SIMPLE and related methods for the solution of Navier-Stokes equations
Просмотров 179Месяц назад
This lecture is about SIMPLE and related methods for the solution of Navier-Stokes equations. This class of methods is most frequently used in both commercial and public CFD codes. After an introduction to principles behind these methods, four algorithms are described in detail: SIMPLE, SIMPLEC, SIMPLER, and PISO. There are more versions of such algorithms in literature, but they differ only in...
17. Fractional-step methods for the solution of Navier-Stokes equations
Просмотров 269Месяц назад
This lecture is about fractional-step methods for the solution of Navier-Stokes equations. The basic ideas behind this class of methods are explained, followed by the description of non-iterative schemes. The issues related to the treatment of convection and viscous terms are highlighted, because they affect both the stability of the method, i.e. the limit on the usable time-step size, and the ...
16. Introduction to solution methods for the Navier-Stokes equations
Просмотров 200Месяц назад
This lecture is about special features of the Navier-Stokes equations which go beyond the generic conservation equation that was considered so far. In preceding lectures, we assumed that the velocity field was known - which is what we normally do when solving scalar transport equations. Now we need to compute the velocity and pressure fields and must deal with the non-linearity and coupling of ...
15. Application examples for simulations of unsteady flows - testing of time integration methods
Просмотров 1772 месяца назад
Note: This video has been updated. I found the reason for the discrepancy between research code and commercial software: the grid was finer in the latter... The plot of 2D grid has been replaced, because it had 160x160 instead of 80x80 cells. Replaced is also the plot in slide 20. In this lecture the performance of some of the time-integration methods described in the two previous two lectures ...
14. Higher-order time advancing methods for unsteady flows
Просмотров 1112 месяца назад
In this lecture, some higher-order methods for time integration are presented. These methods require information from more than two time levels and are therefore called multipoint methods. The additional points may be the time steps at which solution has already been obtained, or auxiliary steps between two time levels. After a brief introduction to the topic, three explicit methods from the Ad...
13. Introduction to solution methods for unsteady flows
Просмотров 1022 месяца назад
This and the next two lectures are devoted to solution methods for unsteady flows. After a brief introduction to flow unsteadiness, the simplest time marching schemes introduced by Euler more than 250 years ago are described. The explicit scheme is never used, but the implicit version is available in each CFD code. Next, midpoint rule for time integration is described, with a focus on the leapf...
12. Application examples for solving linear algebraic equation systems
Просмотров 1292 месяца назад
In this lecture the performance of various solvers is analyzed when applied to 4 test cases representative of equations encountered in CFD. The first test case deals with solution of Laplace equation in two dimensions. For this test case an analytical solution exists, so that iteration errors can be determined at each iteration. The same problem is then studied in three dimensions in the second...
11. Advanced solution methods for linear algebraic equation systems in CFD.
Просмотров 2403 месяца назад
In this lecture the under-relaxation approach is described first. Its aim is to promote the convergence of outer iterations when solving non-linear and coupled equation systems, but it is also important when deferred correction approach is used in conjunction with discretization methods of a high order. Because it modifies the linear algebraic equation system and thus influences also the perfor...
10. Introduction to solution methods for linear algebraic equation systems in CFD
Просмотров 1533 месяца назад
This lecture deals with solution methods for linear algebraic equation systems. Although direct solution methods are seldom used for this purpose in CFD, I first describe two methods because one of them serves as the basis for some iterative solution methods. The next topic are iterative solution methods, which are almost exclusively used to solve algebraic equation systems in CFD. Because ther...
9.Examples of Application of 2nd & 4th-Order Finite-Volume Methods to Solving 2D Transport Equations
Просмотров 1163 месяца назад
Higher-order finite-volume methods require special treatment near boundaries; that is the first topic in this lecture. Described are two approaches: using ghost cells on the outer side of solution domain boundary, and using adapted interpolation and differentiation methods in cells along boundaries. The next topic is the implementation of Dirichlet and Neumann boundary condition in higher-order...
8. Advanced (Higher-Order) Finite-Volume Methods for Computational Fluid Dynamics (CFD)
Просмотров 1933 месяца назад
In this lecture higher-order approximations for finite-volume methods are described. First, Simpson rules for surface integrals in two and three dimensions are described, including the proof for 4th order convergence. The next steps are higher-order interpolation methods, which are required to retain the 4th order of integral approximation when computing convection fluxes. Described are both st...
7. Introduction to Finite-Volume Methods for Computational Fluid Dynamics (CFD)
Просмотров 2863 месяца назад
This lecture is about the principles of finite-volume methods. It begins with a presentation of the basic approximations for surface and volume integrals. The next steps are basic interpolation methods, which are needed to compute convection fluxes, and approximations of gradients at control volume faces, which are needed to compute diffusion fluxes. It is also shown how the order of integral a...
6. Application Examples for FD Methods and Error Analysis
Просмотров 2183 месяца назад
This video is about treatment of boundary conditions in finite-difference methods, especially related to higher-order schemes. Error estimation and verification of the order of the method based on Richardson extrapolation and systematic grid refinement is another important topic. The rest of the video is about the results obtained using different finite-difference methods of 1st, 2nd, 3rd, and ...
5. Advanced Finite-Difference Methods for Computational Fluid Dynamics (CFD)
Просмотров 1803 месяца назад
This video is devoted to advanced finite-difference methods. Shown is the derivation of 3rd and 4th-order finite-difference approximations for the first and second derivative, based on polynomial fitting, as well as the compact high-order schemes. Another important topic is the deferred-correction approach, which allows easier implementation of high-order schemes in implicit solution methods fo...
4. Introduction to Finite-Difference Methods for Computational Fluid Dynamics (CFD)
Просмотров 4404 месяца назад
4. Introduction to Finite-Difference Methods for Computational Fluid Dynamics (CFD)
3. Conservation Equations for Mass, Momentum, and Generic Scalar - Mathematical Models for CFD
Просмотров 4834 месяца назад
3. Conservation Equations for Mass, Momentum, and Generic Scalar - Mathematical Models for CFD
2. Introduction to CFD Methods and Their Properties
Просмотров 9184 месяца назад
2. Introduction to CFD Methods and Their Properties
1. Approaches to Solving Flow Problems and the Role of CFD
Просмотров 1,7 тыс.4 месяца назад
1. Approaches to Solving Flow Problems and the Role of CFD
Introduction to the Lecture Series on CFD by Milovan Peric - Part I
Просмотров 2,3 тыс.4 месяца назад
Introduction to the Lecture Series on CFD by Milovan Peric - Part I
Animation of Large-Eddy Simulation of Flow around a Sphere With a Trip Wire at Re = 50,000
Просмотров 2654 месяца назад
Animation of Large-Eddy Simulation of Flow around a Sphere With a Trip Wire at Re = 50,000
Animation of Large-Eddy Simulation of Flow Around a Smooth Sphere at Re = 50,000
Просмотров 6784 месяца назад
Animation of Large-Eddy Simulation of Flow Around a Smooth Sphere at Re = 50,000
When is the next lecture?
Thank you
Teacher,Could you give me a tutorial that I can finished the project like what you show in the video ?I am a begginer，I dont konw how to start.so I decide to set a goal,for example ,do some classical cfd project like you show even if i dont konw more about the fundamental theorem.
Cool!
Thank you!!!
Thank you professor. I have started this course, and I hope I’ll be able to finish it asap by using my weekends😊
Excellent lecture.
At 13:50 and at 17:35, it remains unexplained "why for the smallest grid spacing the slope reduces". This behaviour is caused by number precision as shown in the truncation_vs_round_off_error github repository. I found that this phenomenon often causes frustration when grid/time-step convergence studies are carried out because when round-off errors start to dominate then convergence cannot be demonstrated anymore.
Thank you
Hello professor I cannot explain how happy I became when I saw this announcement. 🎉🎉🎉 I have been waiting for these lectures since your presence in the Engineering podcast where you mentioned it. THANK YOU SO MUCH🙏🏻🙏🏻🙏🏻🙏🏻
Dear Dr. Peric, Your lecture series is amazing. Thank you very much! Is it possible that after the introduction course you may talk about recent development of PINN on the CFD?
Thank you so much!
Super! Thanks
Hvala puno
Very relaxed explanation but easy to understand
Excellent
Good job
Very nice 🫡🫡
Very good
Previous we had Feynman Lectures on Physics. Now we have Peric Lectures on CFD. WoW!
Hello, Dr. Peric, Greatings from Wei Shan.
Thanks for sharing these amazing contents!
Thanks a lot for sharing!
I hope that at least something of what I am sharing will be useful to at least some people... Once the series work is done, I may start sharing the anecdotes and other fun stuff...
@@MilovanPericCFD This is beyond useful! We are so lucky living in the era of Social network and having around great people like you! Many thanks for your efforts.