[fmegally]

This might seem like a basic question, but I am trying to understand what causes a matrix produced by FVM cell-centered discretization to be asymmetrical.


The way I understand it, because each face has two sides there would always be a symmetry around the diagonal. am i understanding this correctly ? and if yes what conditions causes it to not be symmetric anymore



Thanks in advance

[arjun]

Originally Posted by fmegally

This might seem like a basic question, but I am trying to understand what causes a matrix produced by FVM cell-centered discretization to be asymmetrical.


The way I understand it, because each face has two sides there would always be a symmetry around the diagonal. am i understanding this correctly ? and if yes what conditions causes it to not be symmetric anymore


Thanks in advance

if - else statement causes it:

for example first order upwind would be

if ( flux > 0)
{
value of left cell
}
else
{
value of right cell.
}

[fmegally]

Thanks @arjun. i guess this implies that whenever I use upwind i should use a solver that can handle asymmetry

[FMDenaro]

Think also about a non-uniform grid, you could use central formulas and what you get is a matrix appearing symmetric in the shape but not in the entry values.

[sbaffini]

Originally Posted by FMDenaro

Think also about a non-uniform grid, you could use central formulas and what you get is a matrix appearing symmetric in the shape but not in the entry values.

Yet, a robust FV solver would treat such high order effects with a deferred correction approach, so they would end up in the rhs and not the matrix coefficients