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- W3194050005 abstract "Lagrange algorithm (CLA) for the incompressible Euler equations. Accurate simulations of periodic flow confined in a cylinder with walls are pursued in sight of a recently reported finite time singularity (blow-up) in this geometry. The algorithm exploits the time-analyticity of the particle trajectories of the velocity field. The time-Taylor coefficients of the trajectories fulfill recursion relations and are obtained by solving Helmholtz-Hodge decomposition problems. A Chebyshev-Fourier pseudo-spectral approach to the appearing numerical problems in the underlying cylindrical coordinate system is studied while avoiding unstable spectral differentiation. The appearing Poisson problems are directly solved for the second derivatives of their solutions. For this, a sophisticated Poisson solver, based on modified Bessel functions, is developed and employed. Time-stepping techniques, fixed and adaptive, are proposed and numerically investigated. Furthermore, several methods for the scattered interpolations of the flow fields, known on the particle trajectories after a time step insertion, back onto the fixed grid are reviewed and compared. The presented implementation of the CLA aims for accuracy and is found to be stable and fast also due to the absence of a CFL condition. The latter allows larger time steps and thus reduces tremendously the total number of iterations. Thorough tests on stationary and swirl-free flows are executed and discussed, before a number of simulations of the blow-up candidate from before are inspected. The implementation of the CLA that is presented in this thesis proves to be an excellent tool for fast and accurate incompressible Euler computations in the given geometry." @default.
- W3194050005 created "2021-08-30" @default.
- W3194050005 creator A5079991128 @default.
- W3194050005 date "2020-12-04" @default.
- W3194050005 modified "2023-09-25" @default.
- W3194050005 title "The Cauchy-Lagrange algorithm for axisymmetric incrompressible Euler flow in a wall bounded cylindrical domain : Numerical exploration of regularity loss in the solutions to hydrodynamical equations by high-order semi-Lagrangian methods" @default.
- W3194050005 hasPublicationYear "2020" @default.
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