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

Space-time discontinuous Galerkin finite element method for shallow water flows

A space-time discontinuous Galerkin (DG) finite element method is presented for the shallow water equations over varying bottom topography. The method results in non-linear equations per element, which are solved locally by establishing the element communication with a numerical HLLC flux. To deal with spurious oscillations around discontinuities, we employ a dissipation operator only around discontinuities using Krivodonova's discontinuity detector. The numerical scheme is verified by comparing numerical and exact solutions, and validated against a laboratory experiment involving flow through a contraction. We conclude that the method is second order accurate in both space and time for linear polynomials.\u

Port-Hamiltonian formulation of shallow water equations with Coriolis force and topography

We look into the problem of approximating the shallow water equations with Coriolis forces and topography. We model the system as an infinite-dimensional port-Hamiltonian system which is represented by a non-constant Stokes-Dirac structure. We here employ the idea of using different finite elements for the approximation of geometric variables (forms) describing a distributed parameter system, to spatially discretize the system and obtain a lumped parameter port-Hamiltonian system. The discretized model then captures the physical laws of its infinite-dimensional couterpart such as conservation of energy. We present some preliminary numerical results to justify our claims

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

Modulation of Angiogenesis

This invention relates to compounds, composJtwns, and methods for the treatment of traits, diseases and conditions that respond to the modulation of angiogenic growth factor bioavailability or biological activity

Method of Inhibiting Alu RNA and Therapeutic Uses Thereof

The presently-disclosed subject matter includes methods of identifying an Alu RNA inhibitor, and methods and compo sitions for inhibiting Alu RNA. Methods and compositions can be used for the treatment of geographic atrophy and other conditions of interest

CCR3 Inhibition for Ocular Angiogenesis and Macular Degeneration

Provided are methods and compositions for the treatment or prevention of ocular angiogenesis and neovascularization. Administration of inhibitors of the CCR3 receptor or its ligands eotaxin (CCL11), eotaxin-2 (CCL24) or eotaxin-3 (CCL26) inhibits ocular angiogenesis

Toll like Receptor (TLR) Stimulation for Ocular Angiogenesis and Macular Degeneration

Provided are methods and compositions for the treatment or prevention of ocular angiogenesis and neovascularization. Administration of stimulators of the TLR3 and TLR7 receptors, Trif or of IL-10 and IL-12 inhibits ocular angiogenesis. Furthermore, all siRNAs (both targeted and non-targeted) can inhibit ocular angiogenesis