An immersogeometric formulation for free-surface flows with application to marine engineering problems

• Published in: Computer methods in applied mechanics and engineering Vol. 361; p. 112748
• Main Authors: Zhu, Qiming, Xu, Fei, Xu, Songzhe, Hsu, Ming-Chen, Yan, Jinhui
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.04.2020; Elsevier BV
• Subjects: Algorithms; Boundary conditions; Computational fluid dynamics; Computer simulation; Convection; Dam break; Dirichlet problem; Fluid flow; Free surfaces; Free-surface flows; Immersogeometric method; Incompressible flow; Jacobi matrix method; Level set method; Linear systems; Marine engineering; Mass balance; Multiscale analysis; Planing; Quadratures; Shiphydrodynamics; Solitary waves; Time integration; Immersogeometric method; Shiphydrodynamics; Dam break; Level set method; Free-surface flows
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2019.112748

An immersogeometric formulation is proposed to simulate free-surface flows around structures with complex geometry. The fluid–fluid interface (air–water interface) is handled by the level set method, while the fluid–structure interface is handled through an immersogeometric approach by immersing structures into non-boundary-fitted meshes and enforcing Dirichlet boundary conditions weakly. Residual-based variational multiscale method (RBVMS) is employed to stabilize the coupled Navier–Stokes equations of incompressible flows and level set convection equation. Other level set techniques, including re-distancing and mass balancing, are also incorporated into the immersed formulation. Adaptive quadrature rule is used to better capture the geometry of the immersed structure boundary by accurately integrating the intersected background elements. Generalized-α method is adopted for time integration, which results in a two-stage predictor multi-corrector algorithm. GMRES solver preconditioned with block Jacobian matrices of individual fluid and level set subproblems is used for solving the coupled linear systems arising from the multi-corrector stage. The capability and accuracy of the proposed method are assessed by simulating three challenging marine engineering problems, which are a solitary wave impacting a stationary platform, dam break with an obstacle, and planing of a DTMB 5415 ship model. A refinement study is performed. The predictions of key quantities of interest by the proposed formulation are in good agreement with experimental results and boundary-fitted simulation results from others. The proposed formulation has great potential for wide applications in marine engineering problems. •An immersogeometric formulation for free-surface flow is proposed.•Level set method is adopted for fluid–fluid interface.•FCM with adaptive quadrature is adopted for fluid–structure interface.•An efficient computational algorithm is outlined.•Simulations of marine engineering problems are presented.