The semismooth Newton method for the solution of reactive transport problems including mineral precipitation-dissolution reactions

Abstract

Semismooth Newton method, Quadratic convergence, Complementarity problems, Reactive transport, Mineral precipitation-dissolution,

The semismooth Newton method for multicomponent reactive transport with minerals

“…Note that the versions without elimination and with elimination on the linear level (Section 4.3) are applied in [4]. We obtain I À J Ã 1 ¼ 8 À 6 ¼ 2 decoupled linear scalar PDEs for the g i , I À J Ã 2 ¼ 6 À 5 ¼ 1 constant g i , and a remaining nonlinear system consisting of J kin = 2 discretized PDEs for the n kin,i and J min = 3 PDEs for n A min;i , each living on the active domain of the corresponding mineral n min;i ; the local problems have a size between J mob þ J sorp þ J 2 0 code was implemented by J. Hoffmann using the software platform M++ (Meshes, multigrid and more).…”

“…Having in mind that we want to apply some Newton-like strategy, it is desirable to eliminate the inequalities in (4). For this, a function u : R Â R !…”

“…In [4] a numerical experiment displayed a condition number of system (25) being more than one thousand times lower than the condition number of the system (22)/(23) (even if a diagonal scaling is applied to (22)/ (23)). Hence, the efficiency of iterative solvers is increased, thus motivating the Schur approach.…”

“…The purpose of this section is to demonstrate that the reformulation technique can also be applied when minerals are involved. A model with minerals, but without kinetic and sorption reactions is considered in [4].…”

Solving Partial Differential Algebraic Equations and Reactive Transport Models

“…Semi-smooth Newton methods can be used to solve this difficult problem [4]. From now on, we assume that each mineral is either always totally dissolved (p i = 0) or never totally dissolved (p i > 0) ; with this assumption, the number N p of precipitated species where the threshold is attained is known and fixed, so that the equations above can be rewritten as…”