The nonlinear nature of flow and transport in porous media requires a linearization of the governing numerical-model equations. We propose a new linearization approach and apply it to complex thermal/compositional problems. The key idea of the approach is the transformation of discretized mass- and energy-conservation equations to an operator form with separate space-dependent and statedependent components. The state-dependent operators are parameterized using a uniformly distributed mesh in parameter space. Multilinear interpolation is used during simulation for a continuous reconstruction of state-dependent operators that are used in the assembly of the Jacobian and residual of the nonlinear problem. This approach approximates exact physics of a simulation problem, which is similar to an approximate representation of space and time discretization performed in conventional simulation. Maintaining control of the error in approximate physics, we perform an adaptive parameterization to improve the performance and flexibility of the method. In addition, we extend the method to compositional problems with buoyancy. We demonstrate the robustness and convergence of the approach using problems of practical interest.