%0 Journal Article %1 Ivorra2018 %A Ivorra, Benjamin %D 2018 %J Journal of Scientific Computing %K 76-04-fluid-mechanics-explicit-machine-computation-and-programs 76d05-incompressible-navier-stokes-equations %N 2 %P 1163–1187 %R 10.1007/s10915-017-0489-5 %T 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 %U http://dblp.uni-trier.de/db/journals/jscic/jscic74.html#Ivorra18 %V 74 %X 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.

@article{Ivorra2018, 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.}, added-at = {2019-04-03T01:00:49.000+0200}, author = {Ivorra, Benjamin}, biburl = {https://www.bibsonomy.org/bibtex/2d68653194da252e815751a692bcaab5c/gdmcbain}, day = 01, doi = {10.1007/s10915-017-0489-5}, interhash = {42cd9cb50c7d6d282f01801843825db6}, intrahash = {d68653194da252e815751a692bcaab5c}, issn = {1573-7691}, journal = {Journal of Scientific Computing}, keywords = {76-04-fluid-mechanics-explicit-machine-computation-and-programs 76d05-incompressible-navier-stokes-equations}, month = feb, number = 2, pages = {1163–1187}, timestamp = {2019-04-03T01:00:49.000+0200}, title = {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}, url = {http://dblp.uni-trier.de/db/journals/jscic/jscic74.html#Ivorra18}, volume = 74, year = 2018 }