Port-Reduced Reduced-Basis Component Method for Steady State Navier–Stokes and Passive Scalar Equations

Abstract We develop a Port-Reduced Reduced-Basis Component approach (PR-RBC) to solve partial differential equations (PDEs) that govern incompressible fluid flows in riverine geometries. The PR-RBC method was initially introduced in the literature for linear problems. In this paper, we extend it to a nonlinear context. Our method is presented for the steady state Navier–Stokes problem with an incompressibility constraint. The model is supplemented with a passive scalar equation. We introduce a new method for the treatment of nonlinearity, incompressibility, and convective effects.