The sound field distribution in a room is the consequence of the acoustic properties of radiating sources and the position, geometry and absorbing characteristics of the surrounding boundaries in an enclosure (boundary conditions). Despite there exists a consolidated acoustic wave theory, it is very difficult, nearly impossible, to find an analytical expression of the sound variables distribution in a real room, as function of time and position. This scenario should be seen as an inhomogeneous boundary value problem, where the complexity of source properties and boundary conditions make that problem extremely hard to solve.

Room acoustic simulation, as treated in this thesis, comprises the algebraical approach to solve the wave equation and the way to define the boundary conditions and source modeling of the scenario under analysis.

Numerical methods provide accurate algorithms for this purpose and among the different possibilities, the use of discrete-time methods arises as a suitable solution for solving those partial differential equations, particularized by some specific constrains. Together with the constant growth of the computer power, those methods are increasing their suitability for room acoustic simulation. However, there exists an important lack of accuracy in the definition of some of these conditions so far: current frequency-dependent boundary conditions do not comply with any physical model, and directive sources in discrete-time methods have been hardly treated.

This thesis discusses about the current state-of-the-art of the boundary conditions and source modeling in discrete-time methods for room acoustic simulation and it contributes with some algorithms to enhance boundary condition formulation, in a locally reacting impedance sense, and source modeling in terms of directive sources under a defined radiation pattern. These algorithms have been particularized to some discrete-time methods such as the Finite Difference Time Domain and the Digital Waveguide Mesh.

Regarding to boundary conditions, two different approaches have been followed to achieve a locally reacting impedance boundary condition: one consisting into modify the reflection factor of the boundaries according with the plane wave angle of arrival and the other one, defining these boundaries in terms of the impedance, which is independent from this angle. Both methods have been implemented in a Digital Waveguide Mesh. From the results obtained, advantages and inconveniences are discussed throughout this thesis. Furthermore, based on these new methods, a locally reacting impedance boundary condition is proposed to the Finite Difference Time Domain method, in a similar fashion to the previous one.

On the new topic of directive sources for discrete-time methods, an algorithm based on a multipole expansion is proposed. In a first approach, a method which uses monopoles in order to be adapted to all discrete-time methods for a single frequency is proposed. Later, it has been extended for broadband simulations with a frequency-dependent directivity.