Yanren Hou, Haibiao Zheng
In this paper, an a priori estimate of weak solutions to the mixed Navier-Stokes/Darcy model with Beavers-Joseph-Saffman's interface condition and the existence of a weak solution are established without the small data and/or the large viscosity restriction for the first time. Based on these results, the global uniqueness of the weak solution is obtained.
Wenlong He, Thomas Wick, Xiaohe Yue et al.
We study a fluid-poroelasticity interaction (FPSI) problem coupling the unsteady Stokes equations with the fully dynamic Biot system. A major challenge in such problems is to design partitioned schemes that remain robust in locking-related parameter regimes while preserving the physical interface coupling structure.To address this issue, we introduce two auxiliary variables and reformulate the Biot system as a four-field problem consisting of a dynamic Stokes-like system coupled with a diffusion equation. Crucially, this reformulation preserves the original interface conditions. Based on Robin-Robin transmission conditions with explicitly lagged interface data, we construct a fully decoupled scheme in which the fluid and poroelastic subproblems can be solved independently and in parallel at each time step, without sub-iterations.We prove that the resulting method is unconditionally stable and derive optimal-order error estimates in the $H^1$-norm. The analysis further shows that the scheme is robust with respect to extreme poroelastic parameters and avoids the locking effects inherent in standard formulations. Numerical experiments confirm the theoretical convergence results and demonstrate the locking-robust performance of the proposed method.
Tianhao Chen, Pengbo Xu, Haibiao Zheng
In the field of scientific computing, many problem-solving approaches tend to focus only on the process and final outcome, even in AI for science, there is a lack of deep multimodal information mining behind the data, missing a multimodal framework akin to that in the image-text domain. In this paper, we take Symbolic Regression(SR) as our focal point and, drawing inspiration from the BLIP model in the image-text domain, propose a scientific computing multimodal framework based on Function Images (Funcimg) and Operation Tree Sequence (OTS), named Bootstrapping OTS-Funcimg Pre-training Model (Botfip). In SR experiments, we validate the advantages of Botfip in low-complexity SR problems, showcasing its potential. As a MED framework, Botfip holds promise for future applications in a broader range of scientific computing problems.