Outline of the course objectives. Derivation of the Euler equations (mass and momentum conservation equations).

2.

Derivation of the total energy conservation equation. Recast of the Euler equations in strong conservative form and in vector form. Discrete form vs differential form. Discretization through Taylor series.

3.

Generalized curvilinear coordinates. Euler equations in generalized coordinates.

4.

Creating structured grids using CFDWARP: examples of the various segment types and various commands.

5.

Scalar advection/wave equation. Flux Jacobian and eigenvalues of the Euler equations.

6.

Wave speeds of the Euler equations. How to impose boundary conditions using wave speed theory. Subsonic inflow boundary condition.

Advantage of FDS when resolving boundary layers. Second-order slope-limited schemes: positive coefficients and 1st-order at extrema. Total Variation Diminishing (TVD) schemes

Numerical error vs physical error. How to assess solution convergence error. Determination of discretization error using solutions on two grid levels. Grid Convergence Index (GCI).

13.

Estimate of order of accuracy using 3 mesh levels. Asymptotic range of convergence.