Fluid Mechanics Problem Creating a Mesh

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SUMMARY

The discussion focuses on creating a program for aerodynamic analysis of an airfoil in an Intermediate Fluids class, specifically calculating the surface vectors and area of a triangle given three nodal coordinates (x,y). The area is computed using the determinant formula A=0.5*det([1,1,1;x1,x2,x3;y1,y2,y3]), where x1, x2, and x3 are the x-coordinates and y1, y2, and y3 are the y-coordinates of the triangle's vertices. Additionally, the method for calculating surface vectors involves treating the line between two points as a vector, crossing it with a vector perpendicular to the plane, and normalizing the result.

PREREQUISITES
  • Understanding of basic fluid mechanics concepts
  • Familiarity with MATLAB programming
  • Knowledge of vector mathematics and cross products
  • Ability to compute determinants in linear algebra
NEXT STEPS
  • Learn MATLAB functions for matrix operations and determinants
  • Research vector normalization techniques in MATLAB
  • Explore aerodynamic principles related to airfoil design
  • Study the implementation of cross products in 3D space
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Students in fluid mechanics courses, MATLAB programmers, and engineers involved in aerodynamic analysis and airfoil design.

jboeck6
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We are beginning a project in my Intermediate Fluids class to make a program that can do aerodynamic analysis on an air foil. First, given any three nodal coordinates (x,y) of a triangle, we must write a program to compute its surface vectors and area of the triangle. The nodes will be in clockwise order.

I know I can compute the area through a determinant by doing A=0.5*det([1,1,1;x1,x2,x3;y1,y2,y3]); where 1, 2, and 3 denote each node and x and y are the coordinates.

Please help me start off my code or give insight to calculating the surface vectors.

Also, we will be using MATLAB.

Thanks!
 
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Well you know the direction from anyone point to an adjacent point, right? Treat the line connecting those two as a vector and cross it with a vector coming "out of the page" from the same vertex you started with and you will get a mutually orthogonal vector. Then just normalize it and place it in the center of the line connecting your two points.
 

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