Abstract
In this paper, high-resolution methods for stochastic Buckley Leverett equation and stochastic polymer flooding system are used. The models are augmented with random initial conditions. The numerical solutions are obtained to assess the performance of the methods on the stochastic models of conservation laws for different flow situations. The mean and standard deviation of the stochastic solutions are evaluated. It is investigated that, to what extent recent, the randomness in initial data can affect and be useful in this framework. The consistency, stability and the local truncation error of the methods are proved. Numerical experiments with different scenarios simulate the saturation profile of the models and demonstrating the accuracy of the schemes.
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