Abstract
We propose a novel algorithm for velocity reconstruction from staggered data on arbitrary polygonal staggered meshes. The formulation of the new algorithm is based on a constant polynomial reconstruction approach in conjunction with an iterative defect correction method and is referred to as the IDeC(k) reconstruction. The algorithm is designed for second order accuracy of the reconstructed velocity field and also leads to a consistent estimate of velocity gradients. Accuracy, convergence and robustness of the new algorithm are studied on different mesh topologies and the need for higher-order reconstruction is demonstrated. Numerical experiments for several cases including incompressible viscous flows establish the IDeC(k) reconstruction as a generic, fast, robust and higher-order accurate algorithm on arbitrary polygonal meshes.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 6583-6604 |
| Number of pages | 22 |
| Journal | Journal of Computational Physics |
| Volume | 230 |
| Issue number | 17 |
| DOIs | |
| State | Published - Jul 20 2011 |
Bibliographical note
Funding Information:The first author would like to thank Dr. Dragan Vidović, Institute for the Development of Water Resources, “Jaroslav Černi”, Serbia, for several fruitful discussions that have immensely contributed to this work and Mr. Anoop Cherian, Department of Computer Science and Engineering, University of Minnesota, for his help in analysis of the computational cost of algorithms. The authors are grateful to the reviewers for their insightful comments that have helped improve the manuscript. Computer support from the Minnesota Supercomputing Institute (MSI) is also gratefully acknowledged.
Keywords
- Accuracy
- Arbitrary polygonal meshes
- Defect correction
- Navier-Stokes equations
- Reconstruction
- Staggered mesh