Frequency-dependent Boundary Condition for the 3-d Digital Waveguide Mesh

The three-dimensional digital waveguide mesh is a method for modeling the propagation of sound waves in space. It provides a simulation of the state of the whole soundfield at discrete timesteps. The updating functions of the mesh can be formulated either using physical values of sound pressure or particle velocity, also called the Kirchhoff values, or using a wave decomposition of these instead. Computation in homogenous media is significantly lighter using Kirchhoff variables, but frequency-dependent boundary conditions are more easily defined with wave variables. In this paper a conversion method between these two variable types has been further simplified. Using the resulting structure, a novel method for defining the mesh boundaries with digital filters is introduced. With this new method, the reflection coefficients can be defined in a frequency-dependent manner at the boundaries of a Kirchhoff variable mesh. This leads to computationally lighter and more realistic simulations than previous solutions.