[alibaig1991]

Dear All,

I am looking for reference books and/or articles for vertex-based finite volume method. I know details of cell-centered FVM method which are given in An Introduction to Computational Fluid Dynamics 2nd Edition by Versteeg Malalasekera and The Finite Volume Method in Computational Fluid Dynamics by Darwish M etc.

But these books do not cover mathematical background vertex based FVM. Kindly suggest reference material(s) for this topic.

Thank you.

[praveen]

These books discuss vertex-centered schemes

J. Blazek: Computational Fluid Dynamics: Principles and Applications
https://www.sciencedirect.com/scienc.../9780080999951

R. Lohner: Applied Computational Fluid Dynamics Techniques: An Introduction Based on Finite Element Methods
https://www.wiley.com/en-us/Applied+...-9780470519073

Lohner's book is entirely vertex-based schemes.

[alibaig1991]

Originally Posted by praveen

These books discuss vertex-centered schemes

J. Blazek: Computational Fluid Dynamics: Principles and Applications
https://www.sciencedirect.com/scienc.../9780080999951

R. Lohner: Applied Computational Fluid Dynamics Techniques: An Introduction Based on Finite Element Methods
https://www.wiley.com/en-us/Applied+...-9780470519073

Lohner's book is entirely vertex-based schemes.

I am trying to solve Laplace Equation using 2nd order accurate vertex based FVM. I know about cell centered discretization. The attached file shows the discretization using cell centered approach. Can you help me in deriving the discretized equation using 2nd order accurate vertex based FVM or even 1st order accurate. I can generalize the 1st order accurate scheme to 2nd order scheme myself.

[FMDenaro]

Use the surface integral of the normal derivative and introduce a second order discretization based on the vertex colocation. The source term is a volume integral that you can approximate by mean value formula