“…Many researchers used Eulerian formulation to obtain solutions of such equations (Fennema & Chaudhry, ; Kazezyılmaz‐Alhan & Medina Jr, ; Moussa & Bocquillon, ). Finite difference (Bates, Horritt, & Fewtrell, ; Haltas, Tayfur, & Elci, ; O'brien, Julien, & Fullerton, ), finite volume (Ali, Kimura, & Shimizu, ; Bradford & Sanders, ; Liang et al, ), and finite element (Cobby, Mason, Horritt, & Bates, ; Yu & Lane, ; Zhang, Feng, Maksimović, & Bates, ) schemes are well‐known numerical schemes, among many others. Solutions of Eulerian equations for flood modelling are not always reliable because they often display numerical instabilities or numerical oscillations and also produce artificial diffusions.…”