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Given the complexity of human left heart anatomy and valvular structures, the fluid–structure interaction (FSI) simulation of native and prosthetic valves poses a significant challenge for numerical methods. In this review, recent numerical advancements for both fluid and structural solvers for heart valves in patient-specific left hearts are systematically considered, emphasizing the numerical treatments of blood flow and valve surfaces, which are the most critical aspects for accurate simulations. Numerical methods for hemodynamics are considered under both the continuum and discrete (particle) approaches. The numerical treatments for the structural dynamics of aortic/mitral valves and FSI coupling methods between the solid Ωs and fluid domain Ωf are also reviewed. Future work toward more advanced patient-specific simulations is also discussed, including the fusion of high-fidelity simulation within vivo measurements and physics-based digital twining based on data analytics and machine learning techniques. 

A hybrid computational method coupling the lattice‐Boltzmann (LB) method and a Langevin‐dynamics (LD) method is developed to simulate nanoscale particle and polymer (NPP) suspensions in the presence of both thermal fluctuation and long‐range many‐body hydrodynamic interactions (HIs). Brownian motion of the NPP is explicitly captured by a stochastic forcing term in the LD method. The LD method is two‐way coupled to the nonfluctuating LB fluid through a discrete LB forcing source distribution to capture the long‐range HI. To ensure intrinsically linear scalability with respect to the number of particles, a Eulerian‐host algorithm for short‐distance particle neighbor search and interaction is developed and embedded to LB‐LD framework. The validity and accuracy of the LB‐LD approach are demonstrated through several sample problems. The simulation results show good agreements with theory and experiment. The LB‐LD approach can be favorably incorporated into complex multiscale computational frameworks for efficiently simulating multiscale multicomponent particulate suspension systems such as complex blood suspensions.