We give an overview of recent efforts to model Type Ia supernovae and related astrophysical transients resulting from thermonuclear explosions in white dwarfs. In particular we point out the challenges resulting from the multi-physics multi-scale nature of the problem and discuss possible numerical approaches to meet them in hydrodynamical explosion simulations and radiative transfer modeling. We give examples of how these methods are applied to several explosion scenarios that have been proposed to explain distinct subsets or, in some cases, the majority of the observed events. In case we comment on some of the successes and shortcoming of these scenarios and highlight important outstanding issues.

中文翻译：

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Ia 型超新星和相关天体物理瞬变模型

我们概述了最近为模拟 Ia 型超新星和白矮星热核爆炸引起的相关天体物理瞬变所做的努力。我们特别指出了问题的多物理场多尺度性质所带来的挑战，并讨论了在流体动力学爆炸模拟和辐射传递建模中可能的数值方法来满足这些挑战。我们举例说明这些方法如何应用于几种爆炸场景，这些场景已被提议用于解释不同的子集，或者在某些情况下，解释大多数观察到的事件。如果我们评论这些场景的一些成功和缺点，并强调重要的未决问题。