Type of Publication:  Journal article 
Author:  Leemput, Pieter van; Rheinländer, Martin Kilian; Junk, Michael 
Year of publication:  2009 
Published in:  Computers & Mathematics with Applications ; 58 (2009), 5.  pp. 867882 
DOI (citable link):  https://dx.doi.org/10.1016/j.camwa.2009.02.022 
Summary: 
Lattice Boltzmann methods are paradigmatic discrete evolutions with incomplete initial conditions. This is due to the fact that the variables of the (mesoscopic) method outnumber the variables of the (macroscopic) problem to be solved. In such situations, most initializations which are compatible with the given macroscopic data lead to solutions with oscillatory or steep initial layers. In order to reduce such initial effects, we present a general approach to construct initial values which are compatible with the partial information available, and which guarantee a smooth start of the evolution. Our smoothness condition prescribes the unknown initial values as the polynomial backward extrapolation of the values obtained from a few time steps. Specifically for constant and linear extrapolation, we study the consistency, stability and accuracy of the approach in the case of a lattice Boltzmann method for onedimensional advection. Moreover, the applicability of a simple iteration scheme as the solution method is investigated.

Subject (DDC):  510 Mathematics 
Keywords:  Smooth initialization, Lattice Boltzmann, Constrained runs 
Bibliography of Konstanz:  Yes 
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LEEMPUT, Pieter van, Martin Kilian RHEINLÄNDER, Michael JUNK, 2009. Smooth initialization of lattice Boltzmann schemes. In: Computers & Mathematics with Applications. 58(5), pp. 867882. Available under: doi: 10.1016/j.camwa.2009.02.022
@article{Leemput2009Smoot811, title={Smooth initialization of lattice Boltzmann schemes}, year={2009}, doi={10.1016/j.camwa.2009.02.022}, number={5}, volume={58}, journal={Computers & Mathematics with Applications}, pages={867882}, author={Leemput, Pieter van and Rheinländer, Martin Kilian and Junk, Michael} }