Adaptive Irregular Sampling in Meshfree Flow Simulation

  • Armin Iske
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


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.


Radial Basis Function Smooth Particle Hydrodynamic Thin Plate Spline Meshfree Method Local Error Estimate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media New York 2004

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  • Armin Iske

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