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- Brüger, Armin, et al.
(författare)
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Splitting methods for high order solution of the incompressible Navier-Stokes equations in 3D
- 2005
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Ingår i: International Journal for Numerical Methods in Fluids. - : Wiley. - 0271-2091 .- 1097-0363. ; 47:10-11, s. 1157-1163
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Tidskriftsartikel (refereegranskat)abstract
- The incompressible Navier-Stokes equations are discretized in space by a hybrid method and integrated in time by the method of lines. The solution is determined on a staggered curvilinear grid in two space dimensions and by a Fourier expansion in the third dimension. The space derivatives are approximated by a compact finite difference scheme of fourth-order on the grid. The solution is advanced in time by a semi-implicit method. In each time step, systems of linear equations have to be solved for the velocity and the pressure. The iterations are split into one outer iteration and three inner iterations. The accuracy and efficiency of the method are demonstrated in a numerical experiment with rotated Poiseuille flow perturbed by Off-Sommerfeld modes in a channel.
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- Bruger, A, et al.
(författare)
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High order accurate solution of the incompressible Navier-Stokes equations
- 2005
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Ingår i: Journal of Computational Physics. - : Elsevier BV. - 0021-9991 .- 1090-2716. ; 203:1, s. 49-71
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Tidskriftsartikel (refereegranskat)abstract
- High order methods are of great interest in the study of turbulent flows in complex geometries by means of direct simulation. With this goal in mind, the incompressible Navier-Stokes equations are discretized in space by a compact fourth order finite difference method on a staggered grid. The equations are integrated in time by a second order semi-implicit method. Stable boundary conditions are implemented and the grid is allowed to be curvilinear in two space dimensions. The method is extended to three dimensions by a Fourier expansion. In every time step, a system of linear equations is solved for the velocity and the pressure by an outer and an inner iteration with preconditioning. The convergence properties of the iterative method are analyzed. The order of accuracy of the method is demonstrated in numerical experiments. The method is used to compute the flow in a channel, the driven cavity and a constricted channel.
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| 9. |
- Brüger, Arnim, et al.
(författare)
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High order accurate solution of the incompressible Navier-Stokes equations
- 2003
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- High order methods are of great interest in the study of turbulent flows in complex geometries by means of direct simulation. With this goal in mind, the incompressible Navier-Stokes equations are discretized in space by a compact fourth order finite difference method on a staggered grid. The equations are integrated in time by a second order semi-implicit method. Stable boundary conditions are implemented and the grid is allowed to be curvilinear in two space dimensions. In every time step, a system of linear equations is solved for the velocity and the pressure by an outer and an inner iteration with preconditioning. The convergence properties of the iterative method are analyzed. The order of accuracy of the method is demonstrated in numerical experiments. The method is used to compute the flow in a channel, the driven cavity and a constricted channel.
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- Eliasson, Bengt
(författare)
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Numerical simulation of kinetic effects in ionospheric plasma
- 2001
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis, we study numerically the one-dimensional Vlasov equation for a plasma consisting of electrons and infinitely heavy ions. This partial differential equation describes the evolution of the distribution function of particles in the two-dimensional phase space (x,v). The Vlasov equation describes, in statistical mechanics terms, the collective dynamics of particles interacting with long-range forces, but neglects the short-range "collisional" forces. A space plasma consists of electrically charged particles, and therefore the most important long-range forces acting on a plasma are the Lorentz forces created by electromagnetic fields.What makes the numerical solution of the Vlasov equation to a challenging task is firstly that the fully three-dimensional problem leads to a partial differential equation in the six-dimensional phase space, plus time, making it even hard to store a discretized solution in the computer's memory. Secondly, the Vlasov equation has a tendency of structuring in velocity space (due to free streaming terms), in which steep gradients are created and problems of calculating the v (velocity) derivative of the function accurately increase with time.The method used in this thesis is based on the technique of Fourier transforming the Vlasov equation in velocity space and then solving the resulting equation. We have developed a method where the small-scale information in velocity space is removed through an outgoing wave boundary condition in the Fourier transformed velocity space. The position of the boundary in the Fourier transformed variable determines the amount of small-scale information saved in velocity space.The numerical method is used to investigate a phenomenon of tunnelling of information through an ionospheric layer, discovered in experiments, and to assess the accuracy of approximate analytic formulæ describing plasma wave dispersion. The numerical results are compared with theoretical predictions, and further physical experiments are proposed.
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