Finite Volume Methods: Theorems, Proofs, and Python Implementations (Computational Mathematics Library)

Master conservation-law discretization from first-order upwind to high-order WENO reconstruction with this graduate-level reference that unifies rigorous mathematics and fully executable Python code. Spanning 24 tightly written chapters, the book delivers:• Conservation Laws and Weak Solutions: BV theory, entropy conditions, Rankine–Hugoniot jumps• High-Resolution Schemes: Godunov flux, TVD limiters, WENO and MUSCL reconstructions• Riemann Solvers: Roe, HLL, AUSM with entropy compliance and positivity proofs• Navier–Stokes Applications: Projection methods for incompressible flow and shock-capturing for compressible regimes• Unstructured and Curvilinear Grids: Geometric conservation, median-dual formulations, cubed-sphere examples• Adaptive Mesh Refinement and Multilevel Solvers: Hanging nodes, conservative prolongation, elliptic multigrid• Implicit Newton–Krylov and Parallel Algorithms: Jacobian-free GMRES, domain decomposition scalability• Uncertainty Quantification: Polynomial chaos, multilevel Monte Carlo, mean-square stability analysis Read more