Philip Cardiff

@chenna1985 I cycle by this bridge and plaque on the way to work. I really need to find a reason to use quaternions … maybe beam elements

Quaternions are quite elegant!

@HiroNishikawa Here are profile results of a 3D version of the cavity case using an OpenFOAM incompressible solver from a HPC benchmark project: pressure equation takes 67.9% of the time. Details at wiki.openfoam.com/images/0/00/HP…

Some people told me that the Poisson solver for the pressure correction is the most time-consuming part of an incompressible NS solver while others told me that the Poisson solver is not so expensive and there's no strong need for improvement. I still don't understand it...

@HiroNishikawa I beleive that in many complex geometry RANS cases like this, the outer residuals do not converge per se, but stagnate (with noise), and the user checks the quantities of interest for statistical convergence in some sense, e.g., meancalc.upstream-cfd.com is a tool for this

@HiroNishikawa As a concrete example, in the "motorbike" standard test case in OpenFOAM, which uses SIMPLE (+ kOmegaSST turbulence model), they perform 500 outer iterations (no outer convergence check), with relative tolerances of 0.1 for U/k/omega and 0.01 for p. e.g., develop.openfoam.com/committees/hpc…

It says "solve momentum equations" and "solve pressure correction equation", but I want to know how well they are solved, for example, how many iterations are typically performed to solve these equations. I'm concerned with the details because I often hear that only one or two iterations are performed in practice. So, I wonder whether "solve" means just one or two iterations, or actually reducing the residuals of the discretized equations to a certain level (e.g., 2 or 3 orders of magnitude).

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A Finite Volume Simo-Reissner Beam solver for Moored Floating bodies: sciencedirect.com/science/articl… Important advancement by @ah_taran, with @SeevaniB, led by @phiiliipc with Zeljko Tukovic. #NexSys @MaREIcentre @SEAI_ie @Researchirel @ERC_Research @ichec @UCDmechanics @UCD_Mech_Eng

@HiroNishikawa I am curious to see if you deal with curved boundaries

Finished a draft. It took about three years but I think we were able to improve the original algorithms and also derived new formulas for node-centered schemes. This paper is due May 2026, and so we still have time. Good.

@HiroNishikawa I wonder if there is a definition for “very high order” or “very very high order” in the same way high order is >2. >4 seems like very so maybe over 8 is very very 😜

"p=11" indicates 12th-order accuracy. It's the first time I've seen a code with such a very very high-order scheme.

@HiroNishikawa MATLAB is nice but it will become slow for 2D and 3D (like other non compiled languages) unless you adopt or avoid certain code features eg nested for loops are not good for speed in script languages

At some point, I started to use Matlab for 1D problems. It's very useful. Maybe I should use it also for 2D problems.

@HiroNishikawa What interesting features do spectral collocation method have relative to higher order finite volume or discontinuous Galerkin methods?

A postdoc position is available for CFD algorithm development at Old Dominion University, Norfolk, VA, USA hera.odurf.odu.edu/careers/Career… -- A new high-order positivity-preserving entropy-stable spectral-collocation schemes for 3D compressible Navier-Stokes equations.

@HiroNishikawa How do you calculate the weights? Inverse distance to some power or something else?

Yes for viscous and source terms. For inviscid schemes, we use unweighted LSQ for solver stability.

@HiroNishikawa Exciting. For advection or diffusion or both?

I'm nearing a breakthrough in extending an efficient fourth-order finite volume scheme, originally developed for tetrahedral grids, to mixed-element grids. This is something I thought about and could not figure out for a long time. So, I started to write down the algorithm. An exciting moment in CFD algorithm research.

@HiroNishikawa I wonder if something similar is possible for finite volumes

Interesting database for finite elements

Better late than never. The official group picture from the #ofw20

The 20th #OpenFOAM workshop is started by this years organizer Mirza Popovac #ofw20

@HiroNishikawa If you drop these cross derivative terms, will the order of accuracy be affected? 🤔

This stencil fails because there is no way to determine c4, which is directly related to the cross derivative Pxy, on this stencil. Adding one more point, not on the coordinate axes, will make it work.

@RuaidhriOC @TwoCentsRugby

Been trying to firm this up for a few hours, but here's a bolt from the blue All Black great Carlos Spencer is the new head coach of Terenure College RFC

@HiroNishikawa Using a LSQ fit is interesting; I guess it becomes important for randomly perturbed grids

Yes, if you mean the order of truncation error. It's possible to determine it numerically. Not sure if I can explain this well enough here on X, but I can try once: (1) Write a code that computes your target discrete approximation (residual) at each node/cell in a grid over the domain x=[0,1], e.g., Res_j = ( f_{j+1/2} - f_{j-1/2} )/dx, which approximates df/dx=0 at a node/cell j, where f=f(u), and u is the solution, (2) Choose a smooth function for u, e.g., u(x)=exp(0.5*x), and store it at nodes/cells, u_j=u(x_j) if you define your numerical solution as a point value at x_j, a node or a cell center, (or compute cell averages if you define your numerical solution as a cell average), (3) Compute the residual, Res_j, at each node/cell with the smooth function values that you stored, u_j, j=1,2,3,..., (4) Subtract the value of df/dx at x_j from Res_j, e.g., if f=a*u with a=constant, Res_j = Res_j - a*0.5*exp(0.5*x_j), which should be the truncation error at x=x_j, (5) Compute a norm of Res_j: e.g., L1(Res) = sum_j | Res_j | / N, where N is the total number of nodes/cells, (6) Repeat the process over a series of refined grids, e.g., N=8, 16, 32, etc., and then plot log10( L1(Res) ) versus log10( 1/N ). (7) Slope of the line passing through the data points (or LSQ fit) would be the order of truncation error.

@HiroNishikawa Do you use a symbolic software for this?

Deriving a truncation error of a high-order scheme on a irregular grid. It's very complicated...

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