A NESTED NEWTON-TYPE ALGORITHM FOR FINITE VOLUME METHODS SOLVING RICHARDS' EQUATION IN MIXED FORM

作者：Casulli Vincenzo^*; Zanolli Paola

来源：SIAM Journal on Scientific Computing, 2010, 32(4): 2255-2273.

DOI：10.1137/100786320

• Richards' equation
• variably saturated flow
• finite volume
• mildly nonlinear systems
• Jordan decomposition
• nested iterations

A finite volume discretization of the mixed form of Richards' equation leads to a nonlinear numerical model which yields exact local and global mass conservation. The resulting nonlinear system requires sophisticated numerical strategies, especially in a variable saturated flow regime. In this paper a nested, Newton-type algorithm for the discretized Richards' equation is proposed and analyzed. With a judicious choice of the initial guess, the quadratic convergence rate is obtained for any time step size and for all flow regimes.

• 出版日期2010