Robust layer-resolving methods for the numerical solution of laminar problems in fluid mechanics
John J H MillerMathematics Department, Trinity College, Dublin
Thursday, March 15, 11.00 a.m., CERFACS Conference Room
Abstract :
In this seminar we describe robust layer-resolving methods and explain their importance for practical problems in fluid mechanics. We illustrate their use by constructing and applying such a method to a classical problem in fluid mechanics, which has an "exact" solution in the sense that the problem can be reduced to one involving an ordinary differential equation. To verify that the method is layer-resolving we need to analyse the errors in the numerical approximations to the solution and its derivatives. We describe a new numerical method for the ordinary differential equation, which yields approximations to the "exact" solution and its derivatives having known and guaranteed accuracy. Approximations to the solution and its derivatives of the original problem are then obtained by postprocessing. We outline a strategy for future research in this new area. We give a brief history of "exact" solutions in fluid mechanics and describe the roles of fitted-mesh and fitted-operator methods for solving problems that have non-smooth solutions. We conclude with a short survey of the problems that have been considered to date and the many that remain to be investigated.
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