Author(s): Rahul Saroj Gupta; Prabhakar Akurati; Ritwik Ghoshal; Debneil Nag Chowdhury

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Keywords: Shock-capturing methods; Artificial neural network; Data-driven

Abstract: Different numerical solvers for shock-capturing in fluids face difficulties at discontinuity, causing spurious oscillations and directly impacting the solution's fidelity. Artificial viscosity is one of the techniques that can be used to minimize such oscillations, playing a vital role in dissipating oscillations at the discontinuity. Despite various forms of artificial viscosity models being proposed in contemporary literature, they suffer from a fundamental flaw, viz. their reliance on ad-hoc parameters. We present an approach in this paper that is based on an artificial neural network (ANN) model that has been incorporated into the von Neumann-Richtmyer algorithm. Here, we employ constant predictively determined parameters for artificial viscosity with the broader goal of developing a general-purpose artificial viscosity model for obtaining numerical solutions of initial and boundary-value shock-capture problems. The primary objective of this work is to train these parameters and include them in the numerical approach so that they are both temporally and spatially adaptive. The accuracy of this neural network-based algorithm is presented using numerical results. This approach can accurately capture discontinuities and reduce spurious oscillations, as demonstrated with the help of two standard and well-recognized shock-capture test problems for ideal gas models, viz. the Sod Shock-Tube Problem and the Shu-Osher Shock-Tube Problem, both of which perform with reasonable accuracy, yielding satisfactory results.

DOI: https://doi.org/10.1007/978-981-97-6009-1_59

Year: 2022