输运型概率密度函数（PDF）方法能够精确求解湍流/化学反应相互作用，有望为超燃冲压发动机中复杂的超声速湍流燃烧模拟提供可靠的计算模型。目前超声速流中的概率密度函数方法研究大多局限在简单构型下，严重限制了其在实际超声速燃烧问题中的应用。本文旨在发展基于多块结构网格的曲线坐标概率密度函数方法，使其能适用于具有复杂构型的实际超声速燃烧问题模拟。推导了曲线坐标下的概率密度输运方程和随机微分方程，建立了一般曲线坐标系下的概率密度函数方法及其数值求解框架。提出了多块结构网格下的曲线坐标粒子追踪方法，通过多块网格间的拓扑信息进行粒子局部坐标转换与通信，解决了曲线坐标下粒子局部坐标与全局坐标不一致的问题，成功实现了粒子在全局网格的连续追踪。在一维激波管和二维时间混合层中，通过与精确解和直接数值模拟结果的对比，初步验证了该方法和模型的准确性。进一步在二维圆柱绕流和三维球头绕流算例中，测试了其处理复杂构型的能力。最后开展了典型的超声速同轴射流火焰的数值模拟，与实验结果进行了定量对比。结果显示预测的反应组分与实验符合较好，全面验证了一般曲线坐标系下的概率密度函数方法在实际超声速燃烧问题中的适用性和准确性。

The transported Probability Density Function （PDF） method can accurately solve turbulence/chemical reaction interactions， and can be used as a reliable computational model for complex supersonic turbulent combustion simulations in scramjet engines. At present， research on the PDF method for the supersonic flow is mostly confined to simple configuration， which seriously limits its application in practical supersonic combustion. The objective of this paper is to develop a curvilinear PDF method based on multi-block structured grids， which is applicable to the simulation of real supersonic combustion problems with complex configurations. The PDF equations and stochastic differential equations in curvilinear coordinates are derived， and the PDF method in a general curvilinear coordinate system and its numerical solution framework are established. A method for particle tracking in curvilinear coordinates on the multi-block structural grid is proposed. The topological information between multiple grid blocks is used for particle local coordinate transformation and communication， which solves the problem of inconsistency between particle local coordinates and global coordinates in curvilinear coordinates. Continuous tracking of particles on the global grid is successfully achieved. The accuracy of the curvilinear coordinate method and model is verified by comparing the results with the exact solution and direct numerical simulations in the one-dimensional shock tube and two-dimensional temporal mixing layer. The ability of the method to handle complex configurations is further tested in the simulations of the flow around a two-dimensional cylinder and a three-dimensional spherical blunt. Finally， numerical simulation of a typical supersonic coaxial jet flame is carried out， and the numerical results are quantitatively compared with the experimental results. The comparison results show that the predicted reaction components are in good agreement with those obtained in the experiment， which comprehensively verifies the applicability and accuracy of the PDF method in the general curvilinear coordinate system in actual supersonic combustion problems.