1.2.3.1. Finite Difference and Finite Volume Projects¶

Sod’s Test Problems
2D Heat Transfer using the Finite Volume Method
GAMM Channel

1.2.3.1.1. Sod’s Test Problems ¶

../_images/assignments_sod.png

1.2.3.1.2. 2D Heat Transfer using the Finite Volume Method ¶

1.2.3.1.2.1. Model Equation, Initial Conditions and Boundary Conditions¶

../_images/_0012_Temp_1.png

1.2.3.1.2.2. Grid Generation¶

../_images/_0011_Temp_2.png

1.2.3.1.2.3. Integration wrt Interior Triangles¶

../_images/_0010_Temp_3.png

1.2.3.1.2.4. Strategy¶

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1.2.3.1.2.5. Temporal Term¶

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1.2.3.1.2.6. Laplacian Term¶

../_images/_0007_Temp_6.png

1.2.3.1.2.7. Obtain Fluxes¶

../_images/_0006_Temp_7.png

1.2.3.1.2.8. Corresponding Areas¶

../_images/_0005_Temp_8.png

1.2.3.1.2.9. Update T at the Vertices¶

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1.2.3.1.2.10. Solution at Interior Triangles¶

../_images/_0003_Temp_10.png

1.2.3.1.2.11. Boundary Triangles¶

../_images/_0002_Temp_11.png

1.2.3.1.2.12. Advance in Time¶

../_images/_0001_Temp_12.png

1.2.3.1.2.13. Result¶

../_images/_0000_Temp_13.png

1.2.3.1.3. GAMM Channel ¶

1.2.3.1.3.1. Introduction¶

../_images/GAMM_1.png

1.2.3.1.3.2. Boundary and Initial Conditions¶

../_images/GAMM_2.png

1.2.3.1.3.3. Numerical Method and CFL Condition¶

../_images/GAMM_3.png

1.2.3.1.3.4. Result¶

../_images/GAMM_4.png