Stochastic Solutions for the Two-Dimensional Advection-Diffusion Equation
✍ Scribed by Wan, Xiaoliang; Xiu, Dongbin; Karniadakis, George Em
- Book ID
- 118190511
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 2004
- Tongue
- English
- Weight
- 205 KB
- Volume
- 26
- Category
- Article
- ISSN
- 1064-8275
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## Abstract We prove an optimal‐order error estimate in a weighted energy norm for the modified method of characteristics (MMOC) and the modified method of characteristics with adjusted advection (MMOCAA) for two‐dimensional time‐dependent advection‐diffusion equations, in the sense that the generi
## Abstract A higher‐order accurate numerical scheme is developed to solve the two‐dimensional advection–diffusion equation in a staggered‐grid system. The first‐order spatial derivatives are approximated by the fourth‐order accurate finite‐difference scheme, thus all truncation errors are kept to
Steady and unsteady diffusion equations, with stochastic diffusivity coefficient and forcing term, are modeled in two dimensions by means of stochastic spectral representations. Problem data and solution variables are expanded using the Polynomial Chaos system. The approach leads to a set of coupled