The DGDD method for reduced-order modeling of conservation laws

The discontinuous Galerkin domain decomposition (DGDD) method couples subdomains of high-fidelity polynomial approximation to regions low-dimensional resolution for the numerical solution systems conservation laws. In low-fidelity regions, is approximated by empirical modes constructed Proper Orthogonal Decomposition and a reduced-order model used predict solution. high-dimensional instead solves system laws only in where not amenable representation. coupling between models then performed straightforward manner through fluxes at discrete cell boundaries. We show results from application proposed parametric problems governed quasi-1D 2D compressible Euler equations. particular, we investigate prediction unsteady flows converging-diverging nozzle over NACA0012 airfoil presence shocks. demonstrate stability accuracy significant reduction computational cost with respect model.