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

• The two dimensional advection–diffusion equation in a stochastically varyinggeometry is considered. The varying domain is transformed into a fixed one andthe numerical solution is computed using a high-order finite difference formulationon summation-by-parts form with weakly imposed boundary conditions. Statistics ofthe solution are computed non-intrusively using quadrature rules given by the probabilitydensity function of the random variable. As a quality control, we prove that thecontinuous problem is strongly well-posed, that the semi-discrete problem is stronglystable and verify the accuracy of the scheme. The technique is applied to a heat transferproblem in incompressible flow. Statistical properties such as confidence intervals andvariance of the solution in terms of two functionals are computed and discussed. Weshow that there is a decreasing sensitivity to geometric uncertainty as we graduallylower the frequency and amplitude of the randomness. The results are less sensitiveto variations in the correlation length of the geometry.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Incompressible flow

Advection–diffusion

Uncertainty quantification

Uncertain geometry

Boundary conditions

Parabolic problems

Variable coefficient

Temperature field

Heat transfer

Publication and Content Type

ref (subject category)

art (subject category)