Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 123, Issue 4, Pages 1057-1077Publisher
WILEY
DOI: 10.1002/nme.6888
Keywords
cell-centered finite volume method; eikonal equation; no-inflow boundary condition; polyhedral meshes; signed distance function; Soner boundary condition
Funding
- APVV [19-0460]
- VEGA [1/0436/20, 1/0709/19]
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A cell-centered finite volume method with the Soner boundary condition is proposed for computing the signed distance function in general 3D computational domains. The numerical method is based on the bidirectional time-relaxed eikonal equation and shows second order accuracy in L1 and L infinity-norms. The inclusion of the Soner boundary condition is necessary for numerical solutions to reach the viscosity solution of the eikonal equation in general 3D domains starting from various initial conditions.
A cell-centered finite volume method with the Soner boundary condition is proposed to compute the signed distance function from a given surface in general three-dimensional (3D) computational domains discretized by polyhedral cells. The governing equation is the bidirectional time-relaxed eikonal equation and the proposed numerical method is based on the semi-implicit inflow-implicit and outflow-explicit scheme. Numerical experiments confirm the second order accuracy in L1 and L infinity-norms for chosen examples with smooth solutions. The inclusion of the Soner boundary condition has proven necessary for numerical solutions to reach the viscosity solution of the eikonal equation starting from various initial conditions in general 3D domains.
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