## Abstract

The two dimensional advection–diffusion equation in a stochastically varying geometry is considered. The varying domain is transformed into a fixed one and the numerical solution is computed using a high-order finite difference formulation on summation-by-parts form with weakly imposed boundary conditions. Statistics of the solution are computed non-intrusively using quadrature rules given by the probability density function of the random variable. As a quality control, we prove that the continuous problem is strongly well-posed, that the semi-discrete problem is strongly stable and verify the accuracy of the scheme. The technique is applied to a heat transfer problem in incompressible flow. Statistical properties such as confidence intervals and variance of the solution in terms of two functionals are computed and discussed. We show that there is a decreasing sensitivity to geometric uncertainty as we gradually lower the frequency and amplitude of the randomness. The results are less sensitive to variations in the correlation length of the geometry.

Original language | English |
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Pages (from-to) | 509-529 |

Number of pages | 21 |

Journal | BIT Numerical Mathematics |

Volume | 58 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jun 2018 |

Externally published | Yes |

## Keywords

- Advection–diffusion
- Boundary conditions
- Heat transfer
- Incompressible flow
- Parabolic problems
- Temperature field
- Uncertain geometry
- Uncertainty quantification
- Variable coefficient

## ASJC Scopus subject areas

- Software
- Computer Networks and Communications
- Computational Mathematics
- Applied Mathematics