Papers by Siddhartha Mishra
Communications in Computational Physics, 2015
Applied Mathematical Modelling, 2015
ABSTRACT Two layer Savage-Hutter type shallow water PDEs model flows such as tsunamis generated b... more ABSTRACT Two layer Savage-Hutter type shallow water PDEs model flows such as tsunamis generated by rockslides. On account of heterogeneities in the composition of the granular matter, these models contain uncertain parameters like the ratio of densities of layers, Coulomb and interlayer friction. These parameters are modeled statistically and quantifying the resulting solution uncertainty (UQ) is a crucial task in geophysics. We propose a novel paradigm for UQ that combines the recently developed IFCP spatial discretizations with the recently developed Multi-level Monte Carlo (MLMC) statistical sampling method and provides a fast, accurate and computationally efficient framework to compute statistical quantities of interest. Numerical experiments, including realistic simulations of the Lituya Bay mega tsunami, are presented to illustrate the robustness of the proposed UQ algorithm.
12th European Conference on the Mathematics of Oil Recovery, 2010
Foundations of Computational Mathematics, Hong Kong 2008, 2009
Networks and Heterogeneous Media, 2006
Abstract: We consider a scalar conservation law with a discontinuous flux function. The fluxes ar... more Abstract: We consider a scalar conservation law with a discontinuous flux function. The fluxes are non-convex, have multiple points of extrema and can have arbitrary intersections. We propose an entropy formulation based on interface connections and associated jump conditions at ...
We propose and analyse a finite volume scheme of the Godunov type that preserves discrete steady ... more We propose and analyse a finite volume scheme of the Godunov type that preserves discrete steady states. The scheme works in resonance regime as well as for problems with discontinuous flux. Moreover, no additional modifications of the scheme are required to resolve ...
We consider non-strictly hyperbolic systems of conservation laws in triangular form, which arise ... more We consider non-strictly hyperbolic systems of conservation laws in triangular form, which arise in applications like three-phase flows in porous media. We device simple and efficient finite volume schemes of Godunov type for these systems that exploit the triangular structure. We prove ...
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Papers by Siddhartha Mishra