The continuous progress of reservoir monitoring technology provides encouraging capacities to reduceuncertainties in the subsurface characterization and to mitigate risks in field development applying thereservoir simulation approach. However, it is always challenging to take full advantage of the observationdata, since an accurate representation of strong heterogeneities requires a high-resolution grid. Most ofthe discretization methods cannot handle full tensor permeability, and high nonlinearity introduced bycomplex physical process drastically reduces simulation efficiency. In this work, we develop an advancedparallel framework for reservoir simulation with the implementation of state of the art discretizationand linearization methods. We apply the multipoint flux approximation (MPFA) method to handle thefull tensor permeability in unstructured grids. To keep the fidelity of the geological model and improvecomputational efficiency, we use massively parallel computations via Message Passing Interface (MPI).Complex subsurface physics is described by mass-based formulations making the framework flexible forgeneral-purpose reservoir simulation. However, the representation of phase behavior introduces additionalworkload when compared with the phase-based formulations in the traditional approach. Here, we apply theOperator-Based Linearization (OBL) approach which not only overcomes this drawback but also turns it toan advantage. In this method, the conservation equations are described in an operator form. By constructinga library of tabulated operators, the repeated work spent on complex phase behavior and property evaluationcan be significantly reduced. We benchmark the parallel framework with analytical solutions under single-phase flow and multiphase flow. The results demonstrate that the parallel framework provides accuratesimulation results for structured and unstructured grids. We validate that MPFA implemented in our parallelframework converges to real solutions when the permeability is a full tensor. Besides, several realisticcases have been rigorously tested confirming high computational capacity, efficiency, and accuracy of theadvanced massively parallel framework for general-purpose reservoir simulation. With the implementationof MPFA and OBL approaches, the parallel framework is fully equipped for the simulation of problemswith full tensor permeability, high-heterogeneities, and complex physical processes.