气液两相传热过程广泛存在并常伴随复杂流动现象，本文首先针对复杂两相传热问题开展了高保真两相流传热求解算法研究，并借助开发算法对湍流作用下波浪破碎时的海洋-大气传热问题进行了直接数值模拟研究。对于高雷诺数、大体积比热比两相流传热问题，为保证能量和体积比热两者数值通量求解的一致性，提出了体积比热预估-修正算法，实现了两相流高体积比热比工况下的稳定求解。对于两相传热过程中的相变问题，通过引入速度分解方法，解决了在耦合水平集–体积分数方法下数值模拟气液相变时界面推进不准确的问题，提出了基于该框架下的锐利界面两相流相变模型。最后，应用本文提出的数值传热算法，对湍流作用下波浪破碎时的海洋-大气传热问题进行了直接数值模拟研究, 研究表明波浪运动和大气湍流协同作用产生的非线性效应能够显著强化海洋与大气的热传递，且该协同作用受波龄影响明显。论文主要成果和创新点如下：

本文开发了大体积比热比两相流传热求解算法。为实现大体积比热比两相系统的流动与传热数值模拟，提出了体积比热预估–修正算法。预估步时，采用相同的时间和空间离散格式对体积比热和能量输运方程进行求解，以避免体积比热输运和热量输运解耦。由于采用输运方程求解得到的体积比热没有考虑精准的界面形状，因此需在每个时间步结束时，根据界面位置修正体积比热的分布，以避免体积比热的非物理演化。通过模拟一维液池热扩散、二维绝热液滴对流、以及三维非等温波浪破碎问题，验证了算法的准确性。本文采用速度分解法，基于耦合水平集–体积分数方法框架建立了锐利界面两相流相变模型。通过将流场速度拆分为相变诱导的有势速度和剩余的有旋速度，并将两者分开求解，避免了有势速度和有旋速度数值误差的非线性叠加，显著提升了界面法向量计算的准确性。由于相变时有势速度在界面处沿法向不连续，无法直接用于推进界面指示函数。为解决该问题，本文通过平移源项获得了在界面处连续的体积变化速度，将体积变化速度与有旋速度叠加重构了在界面处连续的界面推进速度。克服了相变发生时界面指示函数推进不正确的难题。通过数值模拟液滴蒸发结果与理论解以及他人结果进行比较，发现新模型的数值计算结果与他人结果吻合，验证了模型的准确性。

最后，将本文提出的数值传热方法应用到传统方法难以模拟的海洋–大气两相流复杂系统的传热问题。采用直接数值模拟方法计算了摩擦雷诺数为180 时波浪破碎过程中的传热问题，系统分析了不同波龄下破碎波对海洋-大气换热的影响机制。模拟波龄设置分别为：3.7（慢速波）、12.0（中速波）以及27.7（快速波）。研究发现，不同波龄下波浪破碎对海面换热影响区别显著。慢速波时，由湍流引起的温度脉动通量主导波面附近温度的上升；快速波时，波浪运动引起的温度脉动通量主导波面附近温度的下降；中速波时，受波浪运动和大气湍流协同作用产生的非线性效应影响，使得波面附近温度下降的幅度和范围较快速波更为显著。

Gas-liquid two-phase flows with heat transfer are ubiquitous and often accompanied by complex flows phenomena. In this paper we propose a robust and high-fidelity numerical method for complex two-fluid heat  transfer problems which is challenging for conventional two-phase flow solvers. Specifically, for high-Reynolds-number two-fluid flows with high-volumetric-heat-capacity contrast, a prediction–correction scheme is implemented to evolve the volumetric heat capacity. The numerical  scheme ensures robust simulations for two-phase flow with high-volumetric-heat-capacity contrasts. For numerical simulation of phase-change problems with sharp interface, a novel phasechange model is proposed using the velocity decomposition method. The total velocity is decomposed into a potential part and a rotational part, which are solved  separately to ensure the numerical stability and accuracy. Finally, as an important application of the proposed method, direct numerical simulations (DNS) are conducted to study the heat transfer in air turbulence over breaking waves. DNS results show that the nonlinear interaction between wave-coherent motion and air turbulence significantly enhances the heat transfer between the ocean and atmosphere, and the nonlinear effect is highly correlated to the wave age. The main results and novelty of the present paper are summarized as follows:

A robust numerical method for heat transfer with high-volumetric-heat-capacity contrasts is developed. To ensure the numerical stability, a prediction–correction scheme is proposed to evolve the transport equation of volumetric heat capacity. In the prediction substep, the volumetric heat capacity is evolved together with the temperature equation. The spatial discretization schemes for the advection term of volumetric heat capacity are consistent with that of temperature to avoid the decoupling of volumetric heat capacity transport and heat transfer. As the volumetric heat capacity obtained from the transport equation does not consider the interface position, it is corrected in accordance with the interface captured by using a coupled level-set and volume-of-fluid (CLSVOF) method at the end of each time step to avoid non-physical evolution. The accuracy of the algorithm is verified by simulating one-dimensional diffusion problem in a still liquid pool, two-dimensional hot droplet convection, and three-dimensional non-isothermal wave breaking.

An interface-resolved phase-change model is proposed based on velocity decomposition. By decomposing the total velocity into the potential part associated with the phase change and the remaining rotational part and solving them separately, the nonlinear superposition of numerical errors between the potential and rotational part is avoided. Because the potential velocity is discontinuous at the interface when phase change occurs, it cannot be used to advance the interface directly. Thus, we construct a continuous velocity at the interface, which is associated with the volume change, by shifting the source term inside the water (or air). As a result, a continuous interface velocity is obtained from adding volume-change velocity and rotational velocity. Verified through the numerical simulation of several benchmark test cases for phase-change problems. The proposed method is found to be accurate and stable.

The developed method is employed to study the heat transfer in wind turbulence over breaking waves, in which the friction Reynolds number is 180. The numerical simulation results are analyzed systematically through the temperature fluctuation fluxes. We have tested three different wave ages, which are 3.7 (slow wave), 12.0 (medium wave), and 27.7 (fast wave). It is found that the effect of wave breaking on heat transfer in wind turbulence is highly associated with wave age. In the slow wave case, the temperature fluctuation flux induced by air turbulence dominates the increase of temperature above the water surface. In the fast wave case, the temperature fluctuation flux caused by wave-coherent motion dominates the decrease of temperature in the near wave region. In the intermediate wave case, the nonlinear effects between the wave motion and air turbulence amplifies the decrease of temperature in the near wave region. As a result, the decrease of temperature in the intermediate wave age is more pronounced than that in fast wave case.