An experimental and numerical study of flow and heat transfer was conducted for a crossed-corrugated geometry, representative of compact heat exchangers under transitional and weakly turbulent conditions. Three-dimensional numerical predictions were obtained by a finite volume method using a variety of approaches ranging from laminar flow assumptions to standard and low-Reynolds number k-epsilon turbulence models, direct simulation, and large-eddy simulation. In this paper, the various computational approaches are presented and their relative performance is discussed for various geometries and Reynolds numbers; results are compared with experimental measurements and literature data. Detailed experimental results are presented in Part I.