In present scenario the applications of numerical reservoir simulators are very wide and extensive. Simulation is the only tool to describe quantitatively multi-phase flow in a heterogeneous reservoir. But, nowadays most of the users of reservoir simulators are becoming the hostages of computer- generated results, even though, many incorrect analysis techniques, mathematical models and computational approaches are used extensively in reservoir simulation study. This paper revealing such incorrect but commonly accepted approaches presents alternate and correct mathematical approaches for the advancement of simulators. First of all authors take privilege of their previous work where, through wide literature survey, various examples (e.g. fracture and shale flow solutions where fine mesh discretization technique may lead to erroneous results due to singular velocities at the fracture and shale tips, fracture flow modeling using discrete point source which was replaced by continuous line source, etc.) of incorrect models were shown and proved to be the source of erroneous results and numerical instability [5]. After revealing such incorrect models, the solutions for eliminating this incorrect techniques and models are presented and proved numerically and analytically. Mathematical techniques and formulations used in this paper are finite element method, finite volume method, advanced conformai mapping, streamfunction and streamline tracing, modern singular integral equation approaches, moving boundary value problems technique, artificial viscosity analysis, generalization of coordinate system, curvilinear grid generation, integral transformations, etc., which stabilize the mentioned simulation models. The recent technological innovations in drilling and production and complicated reservoir studies have challenged the existing simulators so is the key target of this paper is to move in direction of the next generation simulators that can solve the various mentioned inaccuracies. Various accurate mesh generation algorithms are anticipated to develop through this paper to revolutionize the modern reservoir simulation study. Copyright 2012, Society of Petroleum Engineers.