TY - JOUR

T1 - A fast numerical method for ideal fluid flow in domains with multiple stirrers

AU - Nasser, Mohamed M. S.

AU - Green, Christopher C.

PY - 2018/2/7

Y1 - 2018/2/7

N2 - A collection of arbitrarily-shaped solid objects, each moving at a constant speed, can be used to mix or stir ideal fluid, and can give rise to interesting flow patterns. Assuming these systems of fluid stirrers are two-dimensional, the mathematical problem of resolving the flow field - given a particular distribution of any finite number of stirrers of specified shape and speed - can be formulated as a Riemann-Hilbert (R-H) problem. We show that this R-H problem can be solved numerically using a fast and accurate algorithm for any finite number of stirrers based around a boundary integral equation with the generalized Neumann kernel. Various systems of fluid stirrers are considered, and our numerical scheme is shown to handle highly multiply connected domains (i.e. systems of many fluid stirrers) with minimal computational expense.

AB - A collection of arbitrarily-shaped solid objects, each moving at a constant speed, can be used to mix or stir ideal fluid, and can give rise to interesting flow patterns. Assuming these systems of fluid stirrers are two-dimensional, the mathematical problem of resolving the flow field - given a particular distribution of any finite number of stirrers of specified shape and speed - can be formulated as a Riemann-Hilbert (R-H) problem. We show that this R-H problem can be solved numerically using a fast and accurate algorithm for any finite number of stirrers based around a boundary integral equation with the generalized Neumann kernel. Various systems of fluid stirrers are considered, and our numerical scheme is shown to handle highly multiply connected domains (i.e. systems of many fluid stirrers) with minimal computational expense.

KW - fluid stirrers

KW - generalized Neumann kernel

KW - ideal fluid

KW - multiply connected domains

KW - Riemann-Hilbert problem

UR - http://www.scopus.com/inward/record.url?scp=85042528803&partnerID=8YFLogxK

UR - http://purl.org/au-research/grants/arc/DP140100933

U2 - 10.1088/1361-6544/aa99a5

DO - 10.1088/1361-6544/aa99a5

M3 - Article

AN - SCOPUS:85042528803

SN - 0951-7715

VL - 31

SP - 815

EP - 837

JO - Nonlinearity

JF - Nonlinearity

IS - 3

ER -