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Fast and spectrally accurate summation of 2-periodic Stokes potentials
KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
(engelsk)Manuskript (preprint) (Annet vitenskapelig)
##### Abstract [en]

We derive a Ewald decomposition for the Stokeslet in planar periodicity and a novel PME-type O(N log N) method for the fast evaluation of the resulting sums. The decomposition is the natural 2P counterpart to the classical 3P decomposition by Hasimoto, and is given in an explicit form not found in the literature. Truncation error estimates are provided to aid in selecting parameters. The fast, PME-type, method appears to be the first fast method for computing Stokeslet Ewald sums in planar periodicity, and has three attractive properties: it is spectrally accurate; it uses the minimal amount of memory that a gridded Ewald method can use; and provides clarity regarding numerical errors and how to choose parameters. Analytical and numerical results are give to support this. We explore the practicalities of the proposed method, and survey the computational issues involved in applying it to 2-periodic boundary integral Stokes problems.

##### Identifikatorer
OAI: oai:DiVA.org:kth-48803DiVA, id: diva2:458566
QS 2011Tilgjengelig fra: 2011-11-23 Laget: 2011-11-23 Sist oppdatert: 2011-11-25bibliografisk kontrollert
##### Inngår i avhandling
1. Spectral Accuracy in Fast Ewald Methods and Topics in Fluid Interface Simulation
Åpne denne publikasjonen i ny fane eller vindu >>Spectral Accuracy in Fast Ewald Methods and Topics in Fluid Interface Simulation
2011 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
##### Abstract [en]

This work contains two separate but related parts: one on spectrally  accurate and fast Ewald methods for electrostatics and viscous flow,  and one on micro- and complex fluid interface problems.  In Part I we are concerned with fast and spectrally accurate methods  to compute sums of slowly decaying potentials over periodic  lattices. We consider two PDEs: Laplace (electrostatics, the Coulomb  potential) and Stokes (viscous flow, the Stokeslet''  potential). Moreover, we consider both full and planar periodicity,  the latter meaning that periodicity applies in two dimensions and  the third is free''. These are major simulation tasks in current  molecular dynamics simulations and in many areas of computational  fluid mechanics involving e.g. particle suspensions.   For each of the four combinations of PDE and periodic structure, we  give spectrally accurate and O(N log N) fast methods based on  Ewald's or Ewald-like decompositions of the underlying potential  sums. In the plane-periodic cases we derive the decompositions in a  manner that lets us develop fast methods. Associated error estimates  are developed as needed throughout. All four methods can be placed  in the P3M/PME (Particle Mesh Ewald) family. We argue that they  have certain novel and attractive features: first, they are spectral  accurate; secondly, they use the minimal amount of memory possible  within the PME family; third, each has a clear and reliable view of  numerical errors, such that parameters can be chosen  wisely. Analytical and numerical results are given to support these  propositions. We benchmark accuracy and performance versus an  established (S)PME method.  Part II deals with free boundary problems, specifically numerical  methods for multiphase flow. We give an interface tracking method  based on a domain-decomposition idea that lets us split the  interface into overlapping patches. Each patch is discretized on a  uniform grid, and accurate and efficient numerical methods are given  for the equations that govern interface transport. We demonstrate  that the method is accurate and how it's used in immersed boundary,  and interface, Navier-Stokes methods, as well as in a boundary  integral Stokes setting.  Finally, we consider a problem in complex fluidics where there is a  concentration of surfactants \emph{on} the interface and the  interface itself is in contact with a solid boundary (the contact  line problem). We argue that the domain-decomposition framework is  attractive for formulating and treating complex models  (e.g. involving PDEs on a dynamic interface) and proceed with  developing various aspects of such a method.

##### sted, utgiver, år, opplag, sider
Stockholm: KTH Royal Institute of Technology, 2011. s. xv, 104
##### Serie
Trita-CSC-A, ISSN 1653-5723 ; 2011:19
##### Identifikatorer
urn:nbn:se:kth:diva-48805 (URN)978-91-7501-195-0 (ISBN)
##### Disputas
2011-12-16, Salongen, KTHB, Osquars backe 25, Stockholm, 10:00 (engelsk)
##### Forskningsfinansiär
Swedish e‐Science Research Center
QC 20111125Tilgjengelig fra: 2011-11-25 Laget: 2011-11-23 Sist oppdatert: 2012-05-24bibliografisk kontrollert

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arXiv:1111.1815

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##### Av forfatter/redaktør
Lindbo, DagTornberg, Anna-Karin

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Totalt: 124 treff

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