Abstract
We describe the theory and implementation of a three-dimensional fluid dynamics code that we have developed for calculating the surface geometry and circulation currents in the secondaries of interacting binary systems. The main method is based on an Eulerian-Lagrangian scheme to solve the advective and force terms in Euler's equation. Surface normalized spherical polar coordinates are used to allow the accurate modelling of the surface of the star, as is necessary when free surfaces and irradiation effects are to be considered. The potential and its gradient are expressed as sums of Legendre polynomials, which allows a very efficient solution of Poisson's equation. The basic solution scheme, based on operator splitting, is outlined, and standard numerical tests are presented.
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