A unified numerical method based on added momentum source terms for hydrodynamic prediction of underwater vehicles

Classical numerical methods for predicting hydrodynamic coefficients of underwater vehicles typically rely on repeated grid generation, dynamic mesh techniques, and complex physical models, resulting in high computational cost and operational complexity. In this study, a unified numerical method combining added momentum source terms with the Wray-Agarwal 2018 Rotation/Curvature turbulence model (WA-2018 RC model) is developed to address these limitations. The proposed method enables the unified computation of viscous and inertial hydrodynamic coefficients within a single framework. To acquire the desired momentum source terms, the Reynolds-averaged Navier–Stokes (RANS) equations are reformulated in a non-inertial reference frame. The characteristics and implementation of the added momentum source terms are then analyzed. Subsequently, to extend the applicability of the turbulence model to strongly nonlinear flow conditions, the detailed derivation and simplification process of the modified WA-2018 RC model are presented. Numerical discretization schemes for the governing equations, particularly for the source terms, are also developed. The proposed method is validated using two representative cases. The first case investigates the added mass of a sphere and an ellipsoid, where all relative errors between the simulation results and theoretical values are within 6%. The second case evaluates typical linear viscous and inertial hydrodynamic coefficients for the DARPA SUBOFF AFF-8 model, showing that the discrepancy between the simulation results and experimental data is approximately 5%. By employing a single static grid without dynamic mesh techniques and a one-equation turbulence model, the proposed method achieves high computational efficiency, significantly simplifies the implementation process, and reduces computational resource requirements. The method is implemented through secondary development based on the open-source C++ library OpenFOAM-v2012, in which all simulations are conducted.