Ziel
"Many interesting systems in physics and engineering are mathematically modeled by first-order non-linear hyperbolic partial differential equations termed as systems of conservation laws. Examples include the Euler equations of aerodynamics, the shallow water equations of oceanography, multi-phase flows in a porous medium (used in the oil industry), equations of non-linear elasticity and the MHD equations of plasma physics. Numerical methods are the key tools to study these equations and to simulate interesting phenomena such as shock waves.
Despite the intense development of numerical methods for the past three decades and great success in applying these methods to large scale complex physical and engineering simulations, the massive increase in computational power in recent years has exposed the inability of state of the art schemes to simulate very large, multiscale, multiphysics three dimensional problems on complex geometries. In particular, problems with strong shocks that depend explicitly on underlying small scale effects, involve geometric constraints like vorticity and require uncertain inputs such as random initial data and source terms, are beyond the range of existing methods.
The main goal of this project will be to design space-time adaptive \emph{structure preserving} arbitrarily high-order finite volume and discontinuous Galerkin schemes that incorporate correct small scale information and provide for efficient uncertainty quantification. These schemes will tackle emerging grand challenges and dramatically increase the range and scope of numerical simulations for systems modeled by hyperbolic PDEs. Moreover, the schemes will be implemented to ensure optimal performance on emerging massively parallel hardware architecture. The resulting publicly available code can be used by scientists and engineers to study complex systems and design new technologies."
Wissenschaftliches Gebiet
- natural sciencesphysical sciencesplasma physics
- natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations
- natural sciencescomputer and information sciencescomputational sciencemultiphysics
- natural sciencesearth and related environmental sciencesoceanography
- natural sciencesmathematicsapplied mathematicsnumerical analysis
Aufforderung zur Vorschlagseinreichung
ERC-2012-StG_20111012
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Finanzierungsplan
ERC-SG - ERC Starting GrantGastgebende Einrichtung
8092 Zuerich
Schweiz