| Abstract: |
| We investigate a finite volume scheme for the heat equation perturbed by transport noise, a stochastic forcing that models random advection effects and arises naturally in fluid dynamics. The equation is interpreted in the Stratonovich sense, preserving key structural properties such as energy balance at the continuous level.
We introduce a finite volume approximation coupled with an Euler-Maruyama time-splitting discretization with a consistent treatment of the stochastic transport term which is designed to maintain stability and discrete conservation properties. We establish well-posedness of the numerical scheme and prove convergence towards a solution of the stochastic partial differential equation.
Finally, numerical experiments illustrate the behavior of the method, highlighting the impact of transport noise on the solution, in particular on its long-time dynamics. These results demonstrate the robustness and effectiveness of the proposed approach for more complex stochastic diffusion models. |
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