In this series thus far, we have looked at the governing equations of CFD, how to discretise them and what their character is. We have looked at different numerical schemes and how they influence various properties, such as accuracy. Eventually, we need to talk about boundary conditions, as every simulation will have to truncate the …
There are probably as many numerical schemes to solve the discretised Navier-Stokes equations as there are stars in the Milky Way. Well, perhaps a few less. Just have a look at OpenFOAM, and you’ll find over 60 discretisation schemes for the non-linear term in the Navier-Stokes equations. And, while that number seems impressive, I am …
Space and time integration schemes for CFD applications Read More »
When setting up a simulation and running it as an unsteady simulation or even just a steady state simulation with pseudo time stepping, we need to decide if we want to use explicit or implicit time stepping. The choice will have consequences down the line, and we need to be aware of them. In this …
Explicit vs. Implicit time integration and the CFL condition Read More »
In our article on how to derive the Navier-Stokes equations from scratch, I showed you how we can derive the governing equations of fluid mechanics. Once we have found an equation that we want to solve, and we do not have an analytic solution available, we have to approximate a solution to that equation, for …
Did you hear or read somewhere that we can have hyperbolic, parabolic, and elliptic equations in the field of CFD? Did you wonder what these different types are and why you should care about them? If the answer is yes, then this article is for you. In this article, we will look at hyperbolic, parabolic, …
What are Hyperbolic, parabolic, and elliptic equations in CFD? Read More »
Are you looking for a single source that shows you how to derive the Navier-Stokes equations from start to end, without skipping any intermediate steps, and where each intermediate step is explained so that the derivation can be followed? Then look no further, I have written this article to give the most comprehensive review of …
How to Derive the Navier-Stokes Equations: From start to end Read More »
I’ll make a bet with you. By the end of this article, you will have changed your views on numerical dissipation. When you read the words numerical dissipation in the title, did you associate that with something good or bad? My guess is that you view numerical dissipation as something bad, and that would be …
What is numerical dissipation in CFD and why do we need it? Read More »
Have you ever added a CFD solver to your learning to-do list? I have, and it keeps growing! So, instead of creating a to-do list that will never be completed, I thought I’d spend some time on a solver that has been on it for quite some time and share my experiences with you. I …
Have you ever stopped and asked yourself, how do I know if my CFD simulation has actually converged? Well, you are not alone. Judging convergence is one those topics that, at first glance, doesn’t seem to be a very complicated matter, but upon further inspection you realise that this is a deep rabbit hole. In …
How to determine the best stopping criterion for CFD simulations Read More »
