Abstract
Isogeometric analysis (IGA) is combined with the semi-Lagrangian scheme to develop a stable and highly accurate method for the numerical solution of transport problems. An L2 projection using the non-uniform rational B-splines (NURBS) is proposed for the approximation of the solution at the departure points. The proposed method maintains the advantages of the semi-Lagrangian scheme in reducing the truncation errors and allowing for large CFL numbers in the simulations while the IGA guarantees the exact representation of the geometry of the computational domain. The performance of the isogeometric semi-Lagrangian analysis is demonstrated for a deformational flow problem and the benchmark of a single vortex flow.
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