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Application of the Laminar Navier–Stokes Equations for Solving 2D and 3D Pathfinding Problems with Static and Dynamic Spatial Constraints: Implementation and Validation in Comsol Multiphysics

Abstract

Pathfinding problems consist in determining the optimal shortest path, or at least one path, between two points in the space. In this paper, we propose a particular approach, based on methods used in computational fluid dynamics, that intends to solve such problems. In particular, we reformulate pathfinding problems as the motion of a viscous fluid via the use of the laminar Navier–Stokes equations completed with suitable boundary conditions corresponding to some characteristics of the considered problem: position of the initial and final points, a-priori information of the terrain, One-way routes and dynamic spatial configuration. Then, we propose and validate a numerical implementation of this methodology by using Comsol Multiphysics (i.e., a finite element methods software) and by considering various experiments. We compare the obtained results with those returned by a classical pathfinding algorithm. Finally, we perform a sensitivity analysis of the proposed algorithms with respect to some key parameters.

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Correspondence to Benjamin Ivorra.

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This work was carried out thanks to the financial support of the Spanish “Ministry of Economy and Competitiveness” under Projects MTM2011-22658 and MTM2015-64865-P; the “Junta de Andalucía” and the European Regional Development Fund through the Project P12-TIC301; and the research group MOMAT (Ref. 910480) supported by “Banco de Santander” and “Universidad Complutense de Madrid”. The author would like to thank Angel M. Ramos del Olmo and Tatiana Diaz Jimenez for their valuable help during this work.

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Ivorra, B. Application of the Laminar Navier–Stokes Equations for Solving 2D and 3D Pathfinding Problems with Static and Dynamic Spatial Constraints: Implementation and Validation in Comsol Multiphysics. J Sci Comput 74, 1163–1187 (2018). https://doi.org/10.1007/s10915-017-0489-5

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Keywords

  • Pathfinding
  • Computational fluid dynamics
  • Comsol Multiphysics
  • Spatial constraints
  • Artificial intelligence