Speaker
Description
Nonlinear flow models in heterogeneous porous media lead to large algebraic systems whose efficient solution is often limited by strong nonlinearity and heterogeneity. Fully implicit nonlinear solvers can be computationally expensive, while explicit and/or loosely coupled schemes may suffer from stability issues and slow convergence.
In this work, we develop a class of linearly implicit schemes for nonlinear flow problems, in which nonlinear terms are treated using additive linearization strategies, resulting in a sequence of linear systems with a consistent algebraic structure. This formulation enables the systematic construction of linear two-grid preconditioners, significantly reducing both online computational cost. The resulting additive scheme based iteration is interpreted as a preconditioned fixed-point scheme, which is further enhanced using nonlinear acceleration techniques. This combination retains the robustness of implicit approaches while substantially improving convergence rates at low additional cost. Numerical experiments for nonlinear porous-media flow problems demonstrate that the proposed framework provides an effective and scalable approach.