13/04/2017 - 11:00 Mr Chris Eldred (Université Paris 13 (LAGA)) Salle 106 - Batiment IMAG
Many important physical systems are Hamiltonian, and this structure underlies many of the most basic principles we know about nature; such as conservation laws. The equations of inviscid, (moist-)adiabatic fluid dynamics fall into this category, and form the basis of numerical models for climate and weather forecasting (termed dynamical cores). Guided by the philosophy that we are discretizing not arbitrary PDEs, but building representations of physical systems, it is highly desirable that a numerical model possess similar properties to the system under consideration. This can be achieved by retaining key elements of the underlying Hamiltonian structure in the discrete model. A very general approach to the design such methods is outlined: the combination of a Hamiltonian formulation for the continuous equations with a mimetic discretization. Utilizing this approach, it is possible to obtain many desirable properties such as energy conservation, curl-free pressure gradients and the absence of spurious stationary computational modes. For several reasons (principally linear mode properties and higher-order accuracy on arbitrary grids), we have chosen to use a mimetic Galerkin method. Furthermore, by carefully choosing the discrete function spaces, it is possible to simultaneously obtain good computational performance, higher-order accuracy, and many useful mimetic properties such as energy conservation. This talk will present a concrete realization of this philosophy: Dynamico-FE, which is a high-order, structure-preserving hydrostatic dynamical core targeting moderate-resolution climate applications (around 25km in the horizontal). It will also discuss development efforts towards future sound-proof and non-hydrostatic dynamical cores targeting high-resolution, convection permitting climate forecasting, built on the same principles.