Accurate and consistent particle tracking on unstructured grids

• Published in: International journal for numerical methods in fluids Vol. 80; no. 11; pp. 648 - 665
• Main Authors: Ketefian, G. S., Gross, E. S., Stelling, G. S.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 20.04.2016; Wiley Subscription Services, Inc
• Subjects: Accuracy; Advection; Differential equations; Exact solutions; finite volume; Lagrangian transport; Linear systems; Mathematical models; Numerical analysis; Particle tracking; semi-Lagrangian advection; streamlines; unstructured mesh
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.4168

Summary A new numerical method for particle tracking (Lagrangian particle advection) on 2‐D unstructured grids with triangular cells is presented and tested. This method combines key attributes of published methods, including streamline closure for steady flows and local mass conservation (uniformity preservation). The subgrid‐scale velocity reconstruction is linear, and this linear velocity field is integrated analytically to obtain particle trajectories. A complete analytic solution to the 2‐D system of ordinary differential equations (ODEs) governing particle trajectories within a grid cell is provided. The analytic solution to the linear system of locally mass‐conserving constraints that must be enforced to obtain the coefficients in the ODEs is also provided. Numerical experiments are performed to demonstrate that the new method has substantial advantages in accuracy over previously published methods and that it does not suffer from unphysical particle clustering. The method can be used not only in particle‐tracking applications but also as part of a semi‐Lagrangian advection scheme.Copyright © 2015 John Wiley & Sons, Ltd. We present a new 2‐D Lagrangian particle‐tracking method on triangular unstructured grids that is more accurate than previously published methods and does not suffer from unphysical particleclustering. We also present the complete analytic solution to the 2‐D system of ordinary differential equations (ODEs) governing particle tracks, the analytic solution to the linear system oflocally mass‐conserving constraints used to obtain the coefficients in the ODEs, and numerical tests demonstrating the accuracy and mass‐conserving property of the method.