Shu-Jie Li

Beijing Computational Science Research Center | CSRC

A 3-D curved mesh generator is prescribed for converting linear elements to quadratic elements required by high-order methods, which is based on the reconstruction of Cubic Bézier surfaces. Successive curved mesh refinement is also supported by inquiring the middle nodes of the edges and faces of the reconstructed quadratic elements via the Cubic B...

In this paper, the predictor-corrector exponential (PCEXP) time marching scheme,originally developed by S.-J. Li, et al in AIAA-2017-0753 is extended to compute the time-dependent solutions of the compressible Navier-Stokes equations with high-order discon-tinuous Galerkin discretizations in space. The ability of PCEXP scheme that can greatlyrelax...

An efficient multigrid framework is developed for the time marching of steady-state compressible flows with a spatially high-order ( p-order polynomial ) modal discontinuous Galerkin method. The core algorithm that based on a global coupling, exponential time integration scheme provides strong damping effects to accelerate the convergence towards t...

A p-multigrid framework is developed for solving steady-state compressible flows discretized with a p-order spatial discontinuous Galerkin method. The algorithm that based on a global coupling, exponential scheme provides strong damping effects to accelerate the convergence to steady-state solutions, while high-frequency error modes are smoothed ou...

An exponential time-integrator scheme of second-order accuracy based on the predictor-corrector methodology, denoted PCEXP, is developed to solve multi-dimensional nonlinear partial differential equations pertaining to fluid dynamics. The effective and efficient implementation of PCEXP is realized by means of the Krylov method. The linear stability...

This paper is one fruit of my PHD work, a robust 3-D finite volume solver for arbitrarily polyhedral grids. Kinetic flux vector splitting (KFVS) scheme is used along with a new radial based function (RBF) gradient reconstruction method which is more accurate than traditional ones. The resulted solver has been validated through several high-speed fl...

The exponential time-marching scheme works well for turbulent flows.

Progress on development of a scalable, very high-order discontinuous Galerkin (DG) solver named HA3D for arbitrary shaped elements is presented with essential consideration of computational efficency for three-dimensional, real-world problems on both the algorithmic and implementation levels. The expensive computational cost of high-order methods i...

We do fundamentally numerical scheme study with considerations of accuracy and practical computational cost for three-dimensional problems. The spatial accuracy is from the high-order spatial methods such as a modal discontinuous Galerkin (DG) method for 3D arbitrary shaped elements. The time accuracy is achieved by designing new efficient schemes....

An exponential time-integrator scheme of second-order accuracy based on the predictor-corrector methodology, denoted PCEXP, is developed to solve multi-dimensional nonlinear partial differential equations pertaining to fluid dynamics. The effective and efficient implementation of PCEXP is realized by means of the Krylov method. The linear stability...

This paper describes a parallel high-order Discontinuous Galerkin method based on orthogonal basis functions in physical space for arbitrary three-dimensional curved boundary geometry. The physical orthogonal basis are obtained by solving multi-stage linear systems which satisfy the orthogonal properties on arbitrary grids. On curved-boundary surfa...

A Hermite WENO reconstruction-based discontinuous Galerkin method RDG(P1P2), designed not only to enhance the accuracy of discontinuous Galerkin method but also to ensure linear stability of the RDG method, is presented for solving the compressible Euler equations on tetrahedral grids. In this RDG(P1P2) method, a quadratic polynomial solution (P2)...