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Uncertainty propagation of the shock position for hyperbolic PDEs using a sensitivity equation method

Abstract

In this work, we design a method to provide confidence intervals for the position of a discontinuity arising in hyperbolic conservation laws when some of the parameters of the problem are uncertain. This is based on a sensitivity equation method, therefore can be used only if the variance of the uncertain parameters is small. We illustrate how this method works on a simple one-dimensional conservation law: the inviscid Burgers equation. Multiple test cases are defined, some for which the analytical solution is known, in order to test the method.
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Dates and versions

hal-04124225 , version 1 (09-06-2023)

Identifiers

  • HAL Id : hal-04124225 , version 1

Cite

Camilla Fiorini. Uncertainty propagation of the shock position for hyperbolic PDEs using a sensitivity equation method. Finite Volumes for Complex Applications 10 (FVCA10), Oct 2023, Strasbourg, France. ⟨hal-04124225⟩
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