Basic exploration of diffusion equation solvers in distributed computing systems has been a very important issue for computational fluid dynamics (CFD). This paper presents a fundamental study of a distributed computing solution for diffusive phenomena in a P2P enhanced Grid system. We propose a simple distributed system with the architecture of multi-clients and multi-servers (MCMS). Multithreading is implemented on both the client and server nodes, enabling them to communicate. This paper focuses on architecture, model implementation, multithreading, network communication, domain decomposition/composition, problem convergence, fault-tolerance, and dynamic load balancing. A discussion of the results from conducted numerical experiments is useful for performing future intensive CFD computations on Grids.