Multigrid methods; domain decomposition for boundary value problems involving PDEs, WENO reconstruction, Finite volume methods for boundary value problems involving PDEs, Transonic flows, Numerical computation of solutions to systems of equations, Finite volume methods applied to problems in fluid mechanics, curved boundary, NURBS-enhanced finite volume method, secondary reconstruction, Euler equations, Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, Shock waves and blast waves in fluid mechanics, Numerical computation using splines, steady Euler equations, Existence, uniqueness, and regularity theory for incompressible inviscid fluids