Solution of discretized Navier-Stokes equations

karolj · May 6, 2024, 18:15

CFD beginner here. I want to understand how we go from the finite-volume discretized N-S momentum equations to a system of linear equations. I understand that we have to assemble a matrix of coefficients and I did this on paper for a 2D staggered grid but I'm not sure if what I came up with is actually correct, and most online sources seem to gloss over this step. Could someone explain or link to any beginner-friendly resources?

Alex C. · May 6, 2024, 18:26

This process is fairly well explained in many textbook.

An Introduction to Computational Fluid Dynamics by H K Versteeg and W Malalasekera and Finite Volume Methods for Hyperbolic Problems by Randall LeVeque are the one I studied.

Versteeg and Malalasekera gets the job done to walk you through the basic ideas, LeVeque has a good depth, you end up coming back to the examples even when you're seasoned in the field.

FMDenaro · May 7, 2024, 04:50

Other basic CFD textbooks are Anderson and Ferziger, Peric, Street

May 6, 2024, 18:15	Solution of discretized Navier-Stokes equations	#1
karolj New Member Karol Hojka Join Date: May 2024 Posts: 1 Rep Power: 0	CFD beginner here. I want to understand how we go from the finite-volume discretized N-S momentum equations to a system of linear equations. I understand that we have to assemble a matrix of coefficients and I did this on paper for a 2D staggered grid but I'm not sure if what I came up with is actually correct, and most online sources seem to gloss over this step. Could someone explain or link to any beginner-friendly resources?

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May 6, 2024, 18:26		#2
Alex C. Member Join Date: Jul 2013 Posts: 56 Rep Power: 12	This process is fairly well explained in many textbook. An Introduction to Computational Fluid Dynamics by H K Versteeg and W Malalasekera and Finite Volume Methods for Hyperbolic Problems by Randall LeVeque are the one I studied. Versteeg and Malalasekera gets the job done to walk you through the basic ideas, LeVeque has a good depth, you end up coming back to the examples even when you're seasoned in the field.

May 7, 2024, 04:50		#3
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,813 Rep Power: 73	Other basic CFD textbooks are Anderson and Ferziger, Peric, Street