Fission gas release and gaseous swelling in nuclear fuel are driven by the transport of fission gas from within the fuel grains to grain boundaries (intra-granular fission gas release). The process involves gas atom diffusion in conjunction with trapping in and resolution from intra-granular bubbles, and is described mathematically by a system of two partial differential equations (PDE). Under the assumption of equilibrium between trapping and resolution (quasi-stationary approximation) the system can be reduced to a single diffusion equation with an effective diffusion coefficient. Numerical solutions used in engineering fuel performance calculations invariably rely on this simplification. First, we investigate the validity of the quasi-stationary approximation compared to the solution of the general system of PDEs. Results demonstrate that the approximation is valid under most conditions of practical interest, but is inadequate to describe intra-granular fission gas release during rapid transients to relatively high temperatures such as postulated reactivity-initiated accidents (RIA). Then, we develop a novel numerical algorithm for the solution of the general PDE system in time-varying conditions. We verify the PolyPole-2 algorithm against a reference finite difference solution for a large number of randomly generated operation histories including prototypical RIA transients. Results demonstrate that PolyPole-2 captures the solution of the general system with a high accuracy and a low computational cost. The PolyPole-2 algorithm overcomes the quasi-stationary approximation and the concept of an effective diffusion coefficient for the solution of the intra-granular fission gas release problem in nuclear fuel analysis.

裂变气体的释放和气体在核燃料中的溶胀是由裂变气体从燃料颗粒内部到晶粒边界的传输所驱动的（颗粒内裂变气体的释放）。该过程涉及气体原子的扩散，颗粒内气泡的捕获和分离，并由两个偏微分方程组（PDE）进行数学描述。在捕获和分辨率之间的平衡（准静态逼近）的假设下，可以将系统简化为具有有效扩散系数的单个扩散方程。工程燃料性能计算中使用的数值解决方案始终依赖于这种简化。首先，我们与准PDE的一般系统的解相比，研究了准平稳近似的有效性。结果表明，该近似值在大多数具有实际意义的条件下都是有效的，但不足以描述在快速过渡到较高温度（例如假定的反应性事故（RIA））期间，颗粒内裂变气体的释放。然后，我们为时变条件下的通用PDE系统的求解开发了一种新颖的数值算法。我们针对大量随机生成的操作历史（包括原型RIA瞬态）针对参考有限差分解决方案验证了PolyPole-2算法。结果表明，PolyPole-2以高精度和低计算量捕获了通用系统的解决方案。