Family of spectral filters for discontinuous problems
Journal of Scientific Computing
Modeling uncertainty in flow simulations via generalized polynomial chaos
Journal of Computational Physics
Uncertainty quantification for systems of conservation laws
Journal of Computational Physics
Padé-Legendre approximants for uncertainty analysis with discontinuous response surfaces
Journal of Computational Physics
A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainties
Journal of Computational Physics
Evolution of Probability Distribution in Time for Solutions of Hyperbolic Equations
Journal of Scientific Computing
Numerical analysis of the Burgers' equation in the presence of uncertainty
Journal of Computational Physics
Journal of Computational Physics
Generalised Polynomial Chaos for a Class of Linear Conservation Laws
Journal of Scientific Computing
Subcell resolution in simplex stochastic collocation for spatial discontinuities
Journal of Computational Physics
Hi-index | 31.48 |
It is well known that the steady state of an isentropic flow in a dual-throat nozzle with equal throat areas is not unique. In particular there is a possibility that the flow contains a shock wave, whose location is determined solely by the initial condition. In this paper, we consider cases with uncertainty in this initial condition and use generalized polynomial chaos methods to study the steady-state solutions for stochastic initial conditions. Special interest is given to the statistics of the shock location. The polynomial chaos (PC) expansion modes are shown to be smooth functions of the spatial variable x, although each solution realization is discontinuous in the spatial variable x. When the variance of the initial condition is small, the probability density function of the shock location is computed with high accuracy. Otherwise, many terms are needed in the PC expansion to produce reasonable results due to the slow convergence of the PC expansion, caused by non-smoothness in random space.