CFD solvers approximate fluid dynamics equations (e.g., Navier-Stokes or Euler for inviscid flows) via spatial discretization and temporal integration.
Spatial Discretization:
- Finite Difference (FDM): Taylor-based derivatives on structured grids; simple, efficient for regular shapes but struggles with irregularities.
- Finite Volume (FVM): Conserves fluxes over control volumes; versatile for unstructured grids and shocks, common in industry.
- Finite Element (FEM): Variational basis functions; strong for adaptive meshes and multiphysics.
Explicit methods (as in the book) excel in parallel efficiency for aerospace but need stability tweaks.
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