arXiv subjects

Zhen-Guo Yan

Publications and source records attributed to Zhen-Guo Yan.

4 recordsLinked to original sources

arXiv2025

Virtual domain extension for imposing boundary conditions in flow simulation using pre-trained local neural operator

This paper builds up a virtual domain extension (VDE) framework for imposing boundary conditions (BCs) in flow simulation using pre-trained local neural operator (LNO). It creates extended virtual domains to the input function to compensate for the corrosion nature of computational domains during LNO inference, thus turns the implementation of BC into the determination of field values on the extended domain. Several strategies to calculate the field values are proposed and validated in solving numerical examples, including padding operation, direct imposition, pressure symmetry, and optimization by backpropagation, and compared with boundary imposition in traditional solvers. It is found that the large time interval of LNO induces a relatively wide near-boundary domain to be processed, thus imposing BC on only a few nodes near the boundary following the immersed boundary conception in traditional solvers can hardly achieve high accuracy. With appropriate values assigned on the extended virtual domains, VDE can accurately impose BCs and lead to reasonable flow field predictions. This work provides a guidance for imposing BCs reliably in LNO prediction, which could facilitate the reuse of pre-trained LNO in more applications.

physics.flu-dyn↗

arXiv2022

A priori subcell limiting based on compact nonuniform nonlinear weighted schemes of high-order CPR method for hyperbolic conservation laws

This paper develops a shock capturing approach for high-order correction procedure via reconstruction (CPR) method with Legendre-Gauss solution points. Shock regions are treated by novel compact nonuniform nonlinear weighted (CNNW) schemes, which have the same solution points as the CPR method. CNNW schemes are constructed by discretizing flux derivatives based on Riemann fluxes at flux points in one cell and using nonuniform nonlinear weighted (NNW) interpolations to obtain the left and right values at flux points. Then, a priori subcell p-adaptive CNNW limiting of the CPR method is proposed for hyperbolic conservation laws. Firstly, a troubled cell indicator is used to detect shock regions and to quantify solution smoothness. Secondly, according to the magnitude of the indicator, CNNW schemes with varying accuracy orders are chosen adaptively for the troubled cells. The spectral property and discrete conservation laws are mathematically analyzed. Various numerical experiments show that the CPR method with subcell CNNW limiting has superiority in satisfying discrete conservation laws and in good balance between resolution and shock capturing robustness.

math.NA↗

arXiv2021

A priori subcell limiting approach for the FR/CPR method on unstructured meshes

A priori subcell limiting approach is developed for high-order flux reconstruction/correction procedure via reconstruction (FR/CPR) on two-dimensional unstructured quadrilateral meshes. Firstly, a modified indicator based on modal energy coefficients is proposed to detect troubled cells. Then, troubled cells are decomposed into nonuniform subcells and each subcell has one solution point. A second-order finite difference shock-capturing scheme based on nonuniform nonlinear weighted (NNW) interpolation is constructed to calculate troubled cells while smooth cells are calculated by the CPR method. Numerical investigations show that the subcell limiting strategy on unstructured quadrilateral meshes is robust in shock-capturing.

math.NA↗

arXiv2020

Nektar++: Design and implementation of an implicit, spectral/$hp$ element, compressible flow solver using a Jacobian-free Newton Krylov approach

At high Reynolds numbers, the use of explicit in time compressible flow simulations with spectral/$hp$ element discretization can become significantly limited by time step. To alleviate this limitation we extend the capability of the spectral/$hp$ element open-source software framework, Nektar++, to include an implicit discontinuous Galerkin compressible flow solver. The integration in time is carried out by a singly diagonally implicit Runge-Kutta method. The non-linear system arising from the implicit time integration is iteratively solved by the Jacobian-free Newton Krylov (JFNK) method. A favorable feature of the JFNK approach is its extensive use of the explicit operators available from the previous explicit in time implementation. The functionalities of different building blocks of the implicit solver are analyzed from the point of view of software design and placed in appropriate hierarchical levels in the C++ libraries. In the detailed implementation, the contributions of different parts of the solver to computational cost, memory consumption, and programming complexity are also analyzed. A combination of analytical and numerical methods is adopted to simplify the programming complexity in forming the preconditioning matrix. The solver is verified and tested using cases such as manufactured compressible Poiseuille flow, Taylor-Green vortex, turbulent flow over a circular cylinder at $\text{Re}=3900$ and shock wave boundary-layer interaction. The results show that the implicit solver can speed-up the simulations while maintaining good simulation accuracy.

physics.flu-dyn↗