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Researcher profile

Shuyu Sun

Shuyu Sun contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
math.NANumerical Analysisphysics.comp-phComputationMachine Learningphysics.flu-dyn

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Published work

7 published item(s)

preprint2026arXiv

A domain decomposition approach to pore-network modeling of porous media flow

We propose a domain-decomposition pore-network method (DD-PNM) for modeling single-phase Stokes flow in porous media. The method combines the accuracy of finite-element discretizations on body-fitted meshes within pore subdomains with a sparse global coupling enforced through interface unknowns. Local Dirichlet-to-Neumann operators are precomputed from finite-element solutions for each pore subdomain, enabling a global Schur-complement system defined solely on internal interfaces. Rigorous mathematical analysis establishes solvability and discrete mass conservation of the global system. Moreover, we constructively recover classical pore-network models by fitting half-throat conductivities to local Dirichlet-to-Neumann maps, providing a principled bridge between mesh-based and network-based frameworks. Numerical results are presented to demonstrate the validity and effectiveness of the overall methodology.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Coupling-Informed Transport Maps for Bayesian Filtering in Nonlinear Dynamical Systems

A likelihood-free transport filtering method is proposed based on the couplings between state and observation variables. By exploiting a block-triangular structure in the transport map, the analysis step of filtering is reformulated as the minimization of the maximum mean discrepancy (MMD) between the true joint measure and its transport-based approximation. To circumvent the non-convexity in the MMD optimization, we introduce a training-free transport filter method via gradient flows, which leads to an analytic computation for the transport map that implies the steepest descent direction of the MMD. The proposed approach accurately approximates non-Gaussian filtering posteriors and avoids particle collapse. We provide a convergence analysis for the expectation of the MMD between the approximated posterior and the truth posterior. Finally, we extend the method to high-dimensional problems through domain localization. Numerical examples demonstrate the superior performance of our approach over conventional filtering methods in nonlinear, non-Gaussian scenarios.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

A fully discrete energy stable scheme for a phase-field moving contact line model with variable densities and viscosities

In this work, we propose a fully discrete energy stable scheme for the phase-field moving contact line model with variable densities and viscosities. The mathematical model consists of a Cahn-Hilliard equation, a Navier-Stokes equation and the generalized Navier boundary condition for the moving contact line. A scalar auxiliary variable is adopted to transform the governing system into an equivalent form, allowing the double well potential to be treated semi-explicitly. A stabilization term is added to balance the explicit nonlinear term originating from the surface energy at fluid-solid interface. A pressure stabilization method is used to decouple the computation of velocity and pressure. Some subtle implicit-explicit treatments are adopted to deal with convention and stress terms. We establish a rigorous proof of energy stability for the proposed time-marching scheme. Then a finite difference method on staggered grids is used to spatially discretize the constructed time-marching scheme. We further prove that the fully discrete scheme also satisfies the discrete energy dissipation law. Numerical results demonstrate accuracy and energy stability of the proposed scheme. Using our numerical scheme, we analyze the contact line dynamics through a shear flow driven droplet sliding case. Three-dimensional droplet spreading is also investigated on a chemically patterned surface. Our numerical simulation accurately predicts the expected energy evolutions and it successfully reproduces expected phenomena that an oil droplet contracts inwards on a hydrophobic zone and spreads outwards quickly on a hydrophilic zone.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Construction of a minimum energy path for the VT flash model by an exponential time differencing scheme with the string method

Phase equilibrium calculation, also known as flash calculation, plays significant roles in various aspects of petroleum and chemical industries. Since Michelsen proposed his milestone studies in 1982, through several decades of development, the current research interest on flash calculation has been shifted from accuracy to efficiency, but the ultimate goal remains the same focusing on estimation of the equilibrium phase amounts and phase compositions under the given variable specification. However, finding the transition route and its related saddle points are very often helpful to study the evolution of phase change and partition. Motivated by this, in this study we apply the string method to find the minimum energy paths and saddle points information of a single-component VT flash model with the Peng-Robinson equation of state. As the system has strong stiffness, common ordinary differential equation solvers have their limitations. To overcome these issues, a Rosenbrock-type exponential time differencing scheme is employed to reduce the computational difficulty caused by the high stiffness of the investigated system. In comparison with the published results and experimental data, the proposed numerical algorithm not only shows good feasibility and accuracy on phase equilibrium calculation, but also successfully calculates the minimum energy path and and saddle point of the single-component VT flash model with strong stiffness.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Thermodynamically Consistent Darcy-Brinkman-Forchheimer Framework in Matrix Acidization

Matrix acidization is an important technique to enhance oil production at the tertiary recovery stage, and its numerical simulation is never concluded. From one of the earliest models, i.e. the two-scale model (Darcy framework), the Darcy-Brinkman-Forchheimer (DBF) framework is developed by adding Brinkman term and Forchheimer term to the momentum conservation equation. However, in the momentum conservation equation of the DBF framework, porosity is put outside of the time derivation term, which cannot describe the change of porosity well. Thus, this work changes the expression so that the modified momentum conservation equation can satisfy Newton's second law. The modified framework is called improved DBF framework. Furthermore, based on the improved DBF framework, the thermal DBF framework is given by introducing the energy balance equation to the improved DBF framework. Both of the frameworks are verified by the former works through numerical experiments and chemical experiments in labs. Parallelization to the codes of the complicated frameworks is also realized, and good scalability can be achieved.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

A new physics-preserving IMPES scheme for incompressible and immiscible two-phase flow in heterogeneous porous media

In this work we consider a new efficient IMplicit Pressure Explicit Saturation (IMPES) scheme for the simulation of incompressible and immiscible two-phase flow in heterogeneous porous media with capillary pressure. Compared with the conventional IMPES schemes, the new IMPES scheme is inherently physics-preserving, namely, the new algorithm is locally mass conservative for both phases and it also enjoys another appealing feature that the total velocity is continuous in the normal direction. Moreover, the new scheme is unbiased with regard to the two phases and the saturations of both phases are bounds-preserving if the time step size is smaller than a certain value. The key ideas in the new scheme include that the Darcy flows for both phases are rewritten in the formulation based on the total velocity and an auxiliary velocity referring to as the capillary potential gradient, and the total discretized conservation equation is obtained by the summation of the discretized conservation equation for each phase. The upwind strategy is applied to update the saturations explicitly, and the upwind mixed finite element methods are used to solve the pressure-velocity systems which can be decoupled. We also present some interesting examples to demonstrate the efficiency and robustness of the new algorithm.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Numerical approximation of a phase-field surfactant model with fluid flow

Modelling interfacial dynamics with soluble surfactants in a multiphase system is a challenging task. Here, we consider the numerical approximation of a phase-field surfactant model with fluid flow. The nonlinearly coupled model consists of two Cahn-Hilliard-type equations and incompressible Navier-Stokes equation. With the introduction of two auxiliary variables, the governing system is transformed into an equivalent form, which allows the nonlinear potentials to be treated efficiently and semi-explicitly. By certain subtle explicit-implicit treatments to stress and convective terms, we construct first and second-order time marching schemes, which are extremely efficient and easy-to-implement, for the transformed governing system. At each time step, the schemes involve solving only a sequence of linear elliptic equations, and computations of phase-field variables, velocity and pressure are fully decoupled. We further establish a rigorous proof of unconditional energy stability for the first-order scheme. Numerical results in both two and three dimensions are obtained, which demonstrate that the proposed schemes are accurate, efficient and unconditionally energy stable. Using our schemes, we investigate the effect of surfactants on droplet deformation and collision under a shear flow, where the increase of surfactant concentration can enhance droplet deformation and inhibit droplet coalescence.

0 citations0 reviewsNo code linkedOpen access