AI 中文总结
本研究构建了热力学相容的肿瘤生长相场模型，提出了基于MSAV方法的一阶时间离散格式，证明其能量稳定且质量守恒，通过数值实验验证了方法的有效性与理论收敛性。
AI 中文摘要
本研究基于能量变分框架构建了肿瘤生长的热力学相容相场模型，该模型将描述肿瘤演化的Cahn-Hilliard方程、营养物质输运方程与不可压缩Navier-Stokes方程耦合在一起。研究人员提出了一种基于多标量辅助变量（Multiple Scalar Auxiliary Variables, MSAV）方法的一阶时间离散格式，并结合压力校正策略，以高效处理该系统的非线性耦合结构。该格式被严格证明具有无条件能量稳定性和质量守恒性，此外，研究人员还针对肿瘤相场变量、营养物质浓度和流体速度建立了最优一阶时间误差估计。最后，数值实验验证了该方法的有效性、鲁棒性，并确认了理论收敛速率。
英文摘要
This work develops a thermodynamically consistent phase-field model for tumor growth based on the energetic variational framework. The model couples the Cahn-Hilliard equations for tumor evolution and nutrient transport with the incompressible Navier-Stokes equations. A first-order time discretization scheme based on the Multiple Scalar Auxiliary Variables (MSAV) approach together with a pressure-correction strategy is proposed to efficiently handle the nonlinear and coupled structure of the system. The proposed scheme is rigorously proved to be unconditionally energy stable and mass conservative. Furthermore, optimal first-order temporal error estimates are established for the tumor phase-field variable, the nutrient concentration, and the fluid velocity. Finally, numerical experiments demonstrate the effectiveness and robustness of the proposed method and verify the theoretical convergence rates.
