A Chebyshev-Galerkin method for inertial waves
dc.rights.license | CC-BY-NC-ND | |
dc.contributor.advisor | Frank, J.E. | |
dc.contributor.advisor | Maas, L.R.M. | |
dc.contributor.author | Kruseman, A.M.S. | |
dc.date.accessioned | 2016-01-28T18:00:36Z | |
dc.date.available | 2016-01-28T18:00:36Z | |
dc.date.issued | 2016 | |
dc.identifier.uri | https://studenttheses.uu.nl/handle/20.500.12932/21750 | |
dc.description.abstract | We consider the incompressible viscous Navier-Stokes equations for a rotating fluid. In a tilted domain inertial waves converge to a wave-attractor and influence the mean flow. This motivates the numerical simulation of the solution to the Navier-Stokes equations with a Chebyshev-Galerkin method. A Stokes time-marching scheme involves two second-order partial differential equations and guarantees continuity. We develop a Chebyshev-Galerkin method to find a weak solution to a set of separable second-order partial differential equations in a three-dimensional rectangular domain with homogeneous boundary conditions. We consider a spectral method with Chebyshev polynomials as basis functions. Weak solutions of a second-order partial differential equation are obtained by solving a linear system of inner-product matrices, which can be solved in terms of expansion coefficients. Boundary conditions can be satisfied with a superposition of Chebyshev polynomials. This approach is extended to higher dimensions in rectangular domains for separable operators. Chebyshev polynomials are orthogonal with respect to a weighted inner-product. Thus, elegant expressions exist for the mass, first-derivative and stiffness matrices. We show exponential convergence of accuracy with grid-resolution and design fast schemes with linear complexity for the multiplication of the inner-product matrices. We construct diagonal preconditioners for the Laplace-operator in one, two and three dimensions. The preconditioned Poisson-system has a condition number that increases sublinearly with grid-size. This is shown analytically in one dimension and numerically in up to three dimensions. | |
dc.description.sponsorship | Utrecht University | |
dc.format.extent | 2853178 | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | |
dc.title | A Chebyshev-Galerkin method for inertial waves | |
dc.type.content | Master Thesis | |
dc.rights.accessrights | Open Access | |
dc.subject.keywords | Chebyshev, inertial, inertial waves, Chebyshev-Galerkin, numerical, wave-attractor, Poisson, Laplace, Laplacian, Navier-Stokes, Navier, Stokes, pressure, correction | |
dc.subject.courseuu | Mathematical Sciences |