The semismooth Newton method for multicomponent reactive transport with minerals

Kräutle, Serge

doi:10.1016/j.advwatres.2010.10.004

Cited by 37 publications

(38 citation statements)

References 22 publications

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“…An efficient combination of the modified Picard and the Newton method, the Picard/Newton method is proposed in [20]. For the sake of completeness we mention also the accelerated Picard method [21] for Richards' equation and the semi-smooth Newton method [19] and L−method [30] for two-phase flow in porous media, as valuable linearization methods.…”

Section: ∂ T θ(ψ ) − ∇ · (K(θ(ψ ))∇(ψmentioning

confidence: 99%

A study on iterative methods for solving Richards’ equation

2016

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This work concerns linearization methods for efficiently solving the Richards equation, a degenerate elliptic-parabolic equation which models flow in saturated/unsaturated porous media. The discretization of Richards' equation is based on backward Euler in time and Galerkin finite elements in space. The most valuable linearization schemes for Richards' equation, i.e. the Newton method, the Picard method, the Picard/Newton method and the L−scheme are presented and their performance is comparatively studied. The convergence, the computational time and the condition numbers for the underlying linear systems are recorded. The convergence of the L−scheme is theoretically proved and the convergence of the other methods is discussed. A new scheme is proposed, the L−scheme/Newton method which is more robust and quadratically convergent. The linearization methods are tested on illustrative numerical examples.

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Section: ∂ T θ(ψ ) − ∇ · (K(θ(ψ ))∇(ψmentioning

confidence: 99%

A study on iterative methods for solving Richards’ equation

2016

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“…This method is of a higher algorithmic complexity and requires additional reformulation of the model by adding so called complementary conditions. The semismooth Newton method can be applied to two-phase flow or multicomponent transport with much better results compared to Newton's method (see [14][15][16]). …”

Section: Introductionmentioning

confidence: 98%

“…A possible improvement to Newton's method for degenerate problems is the semismooth Newton method [14]. This method is of a higher algorithmic complexity and requires additional reformulation of the model by adding so called complementary conditions.…”

Section: Introductionmentioning

confidence: 99%

A robust linearization scheme for finite volume based discretizations for simulation of two-phase flow in porous media

Radu

Nordbotten

Pop

et al. 2015

Journal of Computational and Applied Mathematics

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a b s t r a c tIn this work we consider a mathematical model for two-phase flow in porous media. The fluids are assumed immiscible and incompressible and the solid matrix non-deformable. The mathematical model for the two-phase flow is written in terms of the global pressure and a complementary pressure (obtained by using the Kirchhoff transformation) as primary unknowns. For the spatial discretization, finite volumes have been used (more precisely the multi-point flux approximation method) and in time the backward Euler method has been employed. We present here a new linearization scheme for the nonlinear system arising after the temporal and spatial discretization. We show that the scheme is linearly convergent. Numerical experiments are presented that sustain the theoretical results.

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“…The scalar constants θ, q 0 , β l , β t > 0 are used to specify some further properties of the given problem; their meaning is described in Subsection 3.1.3. For some additional background material regarding this particular application, we refer the interested reader to [26]. The following strategy is valid for many convection-diffusion PDEs.…”

Section: Applicationmentioning

confidence: 99%

“…The present thesis propagates and investigates similar solution strategies as in [25,26], but it focuses on those reactive systems without kinetic reactions, and where all the (equi-librium) reactions are of aquatic and of mineral type, i.e., no so-called sorption reactions are involved. This restriction allows a less technical presentation, to prove stronger theoretical results, and to exploit the overall structure in a better way so that the resulting algorithm can take full advantage of this structure.…”

Section: Introductionmentioning

confidence: 99%