Port-Hamiltonian discretization for open channel flows

A finite-dimensional Port-Hamiltonian formulation for the dynamics of smooth open channel flows is presented. A numerical scheme based on this formulation is developed for both the linear and nonlinear shallow water equations. The scheme is verified against exact solutions and has the advantage of conservation of mass and energy to the discrete level

Nonlinear structural vibrations by the linear acceleration method

Numerical integration method for calculating dynamic response of nonlinear elastic structure

A theory of post-stall transients in multistage axial compression systems

A theory is presented for post stall transients in multistage axial compressors. The theory leads to a set of coupled first-order ordinary differential equations capable of describing the growth and possible decay of a rotating-stall cell during a compressor mass-flow transient. These changing flow features are shown to have a significant effect on the instantaneous compressor pumping characteristic during unsteady operation, and henace on the overall system behavior. It is also found from the theory that the ultimate mode of system response, stable rotating stall or surge, depends not only on the B parameter but also on other parameters, such as the compressor length-to-diameter ratio. Small values of this latter quantity tend to favor the occurrence of surge, as do large values of B. A limited parametric study is carried out to show the impact of the different system features on transient behavior. Based on analytical and numerical results, several specific topics are suggested for future research on post-stall transients

Space-time discontinuous Galerkin discretization of rotating shallow water equations on moving grids

A space-time discontinuous Galerkin (DG) discretization is presented for the (rotating) shallow water equations over varying topography. We formulate the space-time DG finite element discretization in an efficient and conservative discretization. The HLLC flux is used as numerical flux through the finite element boundaries. When discontinuities are present, we locally apply dissipation around these discontinuities with the help of Krivodonova's discontinuity indicator such that spurious oscillations are suppressed. The non-linear algebraic system resulting from the discretization is solved using a pseudo-time integration with a second-order five-stage Runge-Kutta method. A thorough verification of the space-time DG finite element method is undertaken by comparing numerical and exact solutions. We also carry out a discrete Fourier analysis of the one dimensional linear rotating shallow water equations to show that the method is unconditionally stable with minimal dispersion and dissipation error. The numerical scheme is validated in a novel way by considering various simulations of bore-vortex interactions in combination with a qualitative analysis of PV generation by non-uniform bores. Finally, the space-time DG method is particularly suited for problems where dynamic grid motion is required. To demonstrate this we simulate waves generated by a wave maker and verify these for low amplitude waves where linear theory is approximately valid

Solving nonlinear circuits with pulsed excitation by multirate partial differential equations

In this paper the concept of Multirate Partial Differential Equations (MPDEs) is applied to obtain an efficient solution for nonlinear low-frequency electrical circuits with pulsed excitation. The MPDEs are solved by a Galerkin approach and a conventional time discretization. Nonlinearities are efficiently accounted for by neglecting the high-frequency components (ripples) of the state variables and using only their envelope for the evaluation. It is shown that the impact of this approximation on the solution becomes increasingly negligible for rising frequency and leads to significant performance gains.Comment: 4 pages, 7 figures, approved for publication in IEEE Transactions on Magnetic