Toward a Lagrangian Vector Field Topology
| Autor: | Ronald Peikert, Jürgen Waser, Helwig Hauser, Raphael Fuchs, Benjamin Schindler, Jan Kemmler, Filip Sadlo |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
Field (physics)
Computer science 020207 software engineering 02 engineering and technology Topology 01 natural sciences Computer Graphics and Computer-Aided Design Frame of reference Measure (mathematics) Critical point (mathematics) 010305 fluids & plasmas symbols.namesake Acceleration Critical point (thermodynamics) 0103 physical sciences Jacobian matrix and determinant 0202 electrical engineering electronic engineering information engineering symbols Lagrangian coherent structures Applied mathematics Vector field Eigenvalues and eigenvectors Lagrangian |
| Zdroj: | Computer Graphics Forum. 29:1163-1172 |
| ISSN: | 0167-7055 |
| Popis: | In this paper we present an extended critical point concept which allows us to apply vector field topology in the case of unsteady flow. We propose a measure for unsteadiness which describes the rate of change of the velocities in a fluid element over time. This measure allows us to select particles for which topological properties remain intact inside a finite spatio-temporal neighborhood. One benefit of this approach is that the classification of critical points based on the eigenvalues of the Jacobian remains meaningful. In the steady case the proposed criterion reduces to the classical definition of critical points. As a first step we show that finding an optimal Galilean frame of reference can be obtained implicitly by analyzing the acceleration field. In a second step we show that this can be extended by switching to the Lagrangian frame of reference. This way the criterion can detect critical points moving along intricate trajectories. We analyze the behavior of the proposed criterion based on two analytical vector fields for which a correct solution is defined by their inherent symmetries and present results for numerical vector fields. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|