The notion of bisimulation is an important tool for analysis and synthesis of complex dynamical systems. While the notion of bisimulation for systems described by ordinary differential and difference equations is well studied in the literature, a notion of bisimulation for systems of partial differential and difference equations is practically absent. In this paper, we consider the problem of formulating a notion of bisimulation for a class of dynamical systems described by linear partial difference equations with real constant coefficients. We define two notions of bisimulation, namely, S-bisimulation and Π-induced bisimulation, and provide algebraic characterizations for the same.