10:40
MS28: Analysis and numerical methods for conservation laws with stochastic terms (Part 2)
Chair: Haakon Hoel
10:40
25 mins
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Lagrangian Tracking in Stochastic Fields with Application to Ensemble of Velocity Fields
Samah El Mohtar, Ibrahim Hoteit, Leila Issa, Issam Lakkis, Omar Knio
Abstract: We describe an efficient parallel algorithm for forward and backward tracking of passive particles in stochastic flow fields whose statistics are described are prescribed by an underlying ensemble. The construction is designed to address challenges arising from random resampling procedure applied following each assimilation cycle, which leads to rapid growth in the number of particles. To control this growth, the algorithm incorporates an adaptive binning procedure, which conserves the zeroth, first and second moments of probability (total probability, mean position, and variance). Implementation of the method is illustrated based on results of forward and backward tracking experiments, within a realistic high resolution ensemble assimilation setting of the Red Sea. In particular, the results were used to analyze the effects of the maximum number of particles, the time step, the variance of the ensemble, the travel time, the source location, and history of transport.
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11:05
25 mins
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Well-posedness result for an hyperbolic scalar conservation law with a stochastic force using a finite volume approximation
Caroline Bauzet, Vincent Castel, Julia Charrier, Thierry Gallouët
Abstract: We are interested in the Cauchy problem for a nonlinear hyperbolic scalar conservation law in d>1 space dimensions forced by a multiplicative stochastic noise (in the sense of Itô) and with a general time and space dependent flux-function. An existence and uniqueness result of the stochastic entropy solution of this problem together with the convergence of a finite volume approximation will be presented. Comparing with the existing results on the subject, the true novelty of the present study is the use of the numerical approximation to get both existence and uniqueness of the stochastic entropy solution.
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11:30
25 mins
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Approximation schemes for viscosity solutions of fully nonlinear stochastic partial differential equations
Benjamin Seeger
Abstract: I will present a general framework for constructing approximation schemes for stochastic viscosity solutions of fully nonlinear stochastic partial differential equations. Some specific examples include finite difference schemes and Trotter-Kato splitting formulas. I will also give some applications to studying qualitative behavior and connections with stochastic scalar conservation laws.
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