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Adaptive Irregular Sampling in Meshfree Flow Simulation

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Sampling, Wavelets, and Tomography

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

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Abstract

Meshfree discretizations for partial differential equations (PDEs) have recently gained much attention in many different applications from computational science and engineering, as well as in numerical analysis. These modern discretization methods rely essentially on customized adaptive techniques from irregular sampling. In this chapter, the utility of adaptive irregular sampling for flow simulation, in combination with a recent meshfree advection scheme, is illustrated. To this end, both passive advection and nonlinear advection-diffusion processes are included in our discussion. Two main ingredients of the meshfree advection scheme are the Lagrangian method of characteristics and local scattered data interpolation by polyharmonic splines. Both of these useful concepts are explained in this chapter. Finally, numerical examples show the good performance of the meshfree advection scheme, where particularly the utility of adaptive irregular sampling is demonstrated. To this end, we work with two selected test case scenarios from flow simulation: the slotted cylinder and Burgers’ equation.

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Authors
  1. Armin Iske
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Editors and Affiliations

  1. Department of Mathematics, University of Maryland, 20742, College Park, MD, USA

    John J. Benedetto

  2. Department of Mathematical Sciences, DePaul University, 60614-3250, Chicago, IL, USA

    Ahmed I. Zayed

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Iske, A. (2004). Adaptive Irregular Sampling in Meshfree Flow Simulation. In: Benedetto, J.J., Zayed, A.I. (eds) Sampling, Wavelets, and Tomography. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8212-5_11

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  • DOI: https://doi.org/10.1007/978-0-8176-8212-5_11

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6495-8

  • Online ISBN: 978-0-8176-8212-5

  • eBook Packages: Springer Book Archive

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