The effect of uncertain geometries on advection-diffusion of scalar quantities

• The two dimensional advection-diffusion equation in a stochastically varying geometry is considered. The varying domain is transformed into afixed 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Keyword

incompressible flow

advection-diffusion

uncertainty quantification

uncertian geometry

boundary conditions

parabolic problems

variable coefficient

temperature field

Publication and Content Type

vet (subject category)

rap (subject category)