## 1 Introduction  
Voiced sound production in the human larynx is a complex fluid-structure interaction process in which the forced air from the lungs interacts with vocal fold tissues to initiate sustained vibrations that modulate the glottal airflow. The waveform of the glottal flow sets the important acoustic parameters of the sound source. One of the important research goals in voice production is to understand the interaction mechanism between glottal aerodynamics and vocal fold tissue mechanics. The fluid-structure interaction during normal vocal fold vibrations has been well understood with the myoelastic-aerodynamic theory [1]. During each vibration cycle, a mucosal wave travels from the inferior aspect to the superior of the vocal folds. The glottis, which refers to the space between the two vocal folds, forms a convergent shape during vocal fold opening and a divergent shape during vocal fold closing. This alternative convergent-divergent glottal shape generates a temporal pressure asymmetry inside the glottis, which ensures sustained energy transfer from airflow to vocal fold tissues to sustained vibrations. In voice disorders, however, this vibration pattern would be disrupted. Voice disorders are often associated with vocal fold pathologies, such as nodule, cyst, scar, paralysis, and so forth. These pathologies alter the geometry and material properties of vocal fold tissues, resulting in irregular mucosal waves. In these conditions, the glottis during vibrations often exhibits irregular shapes [2]. For example,the glottal channel is often curved from the inferior to superior due to left-right asymmetry. For another example, a multi-channel configuration is often generated due to partial contact of the two vocal folds, which are supposed to be in full contact at the end of the vibration cycle to fully close the glottis. How these irregular glottal shapes affect fluid-structure interactions and the final voice outcome is not well understood. Such understanding is important to elucidate the fundamental mechanism of irregular vocal fold vibrations associated with vocal fold pathologies. Computer models have been playing an important role in understanding the physics of voice production. The very first computer model of voice production was the two-mass model, which modeled each vocal fold as a system of two coupled, spring-mass dampers [3]. The mathematical formulation of the two-mass model was revolutionary in that it provided a very simple and computationally effective manner for computing vocal fold dynamics. The model has been extensively used for studying the physics of voice production in both normal and pathological conditions [4; 5; 6; 7; 8; 9; 10]. A shortcoming of this type of model is the lack of physiological correlation between tissue properties and model system parameters [11; 12]. Although some effort has been made to establish these relationships [13; 14], direct clinical applications are still difficult because a realistic representation of laryngeal physiology is often required in clinics. Continuum vocal fold models improved upon the lumped-mass model by being able to incorporate the realistic morphology and material properties of vocal folds, therefore having a great potential for clinical applications. While continuum vocal fold models have been greatly improved from simple 2D configurations and isotropic materials to highly complex 3D subject-specific geometries and anisotropic materials [15; 16; 17; 18; 19], their use in simulating vocal pathologies is still very limited due to a lack of an accurate and rapid computation of flow pressures in highly irregular glottal shapes. The Bernoulli equation has been dominantly used for its simplicity but it relies on the assumption of symmetric, inviscid one-dimensional (1D) flow and single-channel glottal shape [20; 21; 22].