In this seminar, I will motivate the importance of thermonuclear (Type Ia) supernovae to cosmological studies of dark energy and highlight the open research topic surrounding how these stellar explosions originate from white dwarf (WD) stars. I will then discuss the nature of matter within WD interiors and how some of the important physical processes work that determine WD evolution. Along the way, I will note some of the challenges in modeling WD stars computationally and provide a general overview of how such computations are carried out. This talk will be accessible to graduate students familiar with numerical methods in fields other than astrophysics who might be curious about how stars work, how they explode, and how to predict properties of the explosions.