Identifying Space-Dependent Coefficients and the Order of Fractionality in Fractional Advection–Diffusion Equation
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- 作者：Boris Maryshev ; Alain Cartalade ; Christelle Latrille…
- 关键词：Anomalous transport ; Parameter identification ; Adjoint state method ; Space ; dependent coefficients
- 刊名：Transport in Porous Media
- 出版年：2017
- 出版时间：January 2017
- 年：2017
- 卷：116
- 期：1
- 页码：53-71
- 全文大小：
- 刊物类别：Earth and Environmental Science
- 刊物主题：Geotechnical Engineering & Applied Earth Sciences; Industrial Chemistry/Chemical Engineering; Hydrology/Water Resources; Civil Engineering; Hydrogeology; Classical and Continuum Physics;
- 出版者：Springer Netherlands
- ISSN：1573-1634
- 卷排序：116
文摘
Tracer tests in natural porous media sometimes show abnormalities that suggest considering a fractional variant of the advection–diffusion equation supplemented by a time derivative of non-integer order. We are describing an inverse method for this equation: It finds the order of the fractional derivative and the coefficients that achieve minimum discrepancy between solution and tracer data. Using an adjoint equation divides the computational effort by an amount proportional to the number of freedom degrees, which becomes large when some coefficients depend on space. Method accuracy is checked on synthetical data, and applicability to actual tracer test is demonstrated.