Numerical Methods for Valuation and Optimal Operation of Natural Gas Storage
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The thesis describes different approaches for solving numerically a PDE model for the valuation and optimal operation of a natural gas storage facility, characterized as a Hamilton Jacobi Bellman (HJB) equation. The HJB equation is derived by formulating the given natural gas storage problem as a stochastic control problem and then applying the dynamic programming principle. We present three separate numerical methods for solving the HJB equation, namely a standard upwind finite difference method and two new methods characterized as: (i) a semi-Lagrange time stepping method combined with a one dimensional finite element method, and (ii) a two dimensional finite element method combined with finite difference discretization in time. The upwind finite difference method is shown to be consistent, stable and monotone. These properties guarantee that the numerical solution converge to the viscosity solution of the HJB equation. Numerical results suggest that the two new methods converge to the same solution as the upwind finite difference method for a given test case.