A numerical model, ISWFoam with a modified k-ω SST model, established by combining the density transport equation with a fully three-dimensional (3D) Navier-Stokes equation, is developed to simulate ISWs in continuously stratified, incompressible, viscous fluids based on the open source code OpenFOAM-v1906. ISWFoam provides two initial wave generation methods to generate an ISW in continuously stratified fluids, including solving the weakly nonlinear models of the extended Korteweg-de Vries (eKdV) equation and the fully nonlinear models of the Dubreil-Jacotin-Long (DJL) equation.