Happy Valentine's Day
Today was a reasonably low key Valentine's Day for me. I had my CFD (computational fluid dynamics) class this morning, and I subsequently proceeded to start the coding for my CFD quarter project in earnest. We are supposed to solve the Navier-Stokes equations and the energy equation (with the Bousinessq approximation) using a staggered mesh. The goal of the project is to study the thermal stability (or lack thereof) of a fluid in a box at various Rayleigh numbers. The biggest headache thus far seems to be keeping track of all the indices used throughout the various meshes that are staggered. Quite a book-keeping chore that is.
After working through the afternoon on the project, I walked up to Rite-Aid to buy Ariele a Valentine's Day card. Now that was a sight. I would guess eight to ten people were browsing through the Valentine's Day card section, one of whom was female. Exactly what I would have expected. I then got home, went with Ariele to the gym before dinner, and then we ate. We decided last week to postpone our Valentine's Day dinner out and about until this weekend, because Ariele has a three day conference in Long Beach that she has been driving to and from since Sunday, and the beginning part of the week is a disaster for me as far as homeworks and my weekly research meeting is concerned.
I hope everyone had a happy Valentine's Day.
6 Comments:
Nothing like spending Valentine's Day in the gym with a bunch of sweaty guys and old women...
Is a staggered mesh a mesh that gets refined (smaller spacing) at places that have rapid variation in the quantities being simulated? Or something else entirely?
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A staggered mesh in this sense is two structured (i.e. Cartesian) meshes that are staggered slightly so that the grid points are offset by half the width of one element in both the x and y directions (where dx=dy for each element). You can think of a four-by-four Cartesian mesh with a three-by-three Cartesian mesh embedded such that the geometric centers of both meshes coincide. This larger, staggered mesh then stores values of the x-velocity on the left face of each cell, the y-velocity on the bottom face of each cell, and the pressure at the center of each cell (along with other quantities at each location, of course).
How does all of this work?
Well, it is much too involved to explain in a blog comment, but the algorithm involves using matrices to map data from one portion of the staggered mesh to another portion. A clever construction of these operators allow for the automatic imposition of the conservation of mass constraint, and then it is on to solving the equation of motion and the energy equation. Theoretically, the task is straight forward. Computationally, the book-keeping is quite an obstacle.
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