Integrating finite difference schemes for scalar and vector wave equations

Room acoustic simulation is the process of generating approximate solutions to either the linearized Euler equations or the scalar wave equation. As for the continuous equations, the discrete approximations of both are equivalent. The vector formulation is less efficient, but it can inform several unexploited features of the scalar formulation. This paper first demonstrates the equivalence of the two schemes and explores how the vector formulation may be integrated into the more efficient scalar formulation to produce local velocity estimates and velocity sources on the pressure grid.