This paper proposes a new modeling and solution method that is relatively simple yet powerful enough to handle complex multi-physics problems. The new methodology is based on a combination of cellular automata, finite difference, and analytical analysis concepts. The basic idea is to construct a cascading sequence of simple, explicit rules of evolution, rather than attempt to solve complicated partial differential equations. The resulting scheme is computationally explicit yet numerically stable. In addition to significant modeling flexibility, the cellular automata environment lends itself to extremely efficient computational algorithms and hardware implementation due to its inherent use of local rules and potential for parallel computation. The power and flexibility of the method is demonstrated by developing solutions for a general transport process consisting of elementary processes due to diffusion, advection, reaction kinetics, and external interaction. Explicit and numerically stable rules for each of these elementary processes are developed. Case studies produce physically realistic and numerically accurate solutions for complex processes. Numerical experiments show that the method is highly accurate if the time step is sufficiently small. The value of the method is that a library of rules for simple, elementary processes can be derived individually. These processes can be assembled in a modular manner in any combination to create models for complex processes. The method is currently being used in a number of applications, including a study of complex thermal/mechanical phenomena at the sliding contacts between rubbing surfaces.