Wei Yan

It is well known that for the Eulerian equations the numerical schemes that can accurately capture contact discontinuity usually suffer from some disastrous carbuncle phenomenon, while some more dissipative schemes, such as the HLL scheme, are free from this kind of shock instability. Hybrid schemes to combine a dissipative flux with a less dissipa...

This paper investigates solution behaviors under the strong shock interaction for moving mesh schemes based on the one-dimensional HLL-type Riemann solvers. Numerical experiments show that some schemes which updates the flow parameters directly on the moving mesh without using interpolation, may suffer from severe instability such as grid distortio...

This article presents a new cell-centered numerical method for compressible flows on arbitrary unstructured meshes. A multi-dimensional Riemann solver based on the HLLC method (denoted by HLLC-2D solver) is established. The work is an extension from the cell-centered Lagrangian scheme of Maire et al. [27] to the Eulerian framework. Similarly to the...

This paper investigates solution behaviors under the strong shock interaction for moving mesh schemes based on the one-dimensional Godunov and HLLC Riemann solvers. When the grid motion velocity is close to Lagrangian one, these Godunov methods, which updates the flow parameters directly on the moving mesh without using interpolation, may suffer fr...

The carbuncle phenomenon has been regarded as a spurious solution produced by most of contact-preserving methods. The hybrid method of combining high resolution flux with more dissipative solver is an attractive attempt to cure this kind of non-physical phenomenon. In this paper, a matrix-based stability analysis for 2-D Euler equations is performe...

In this paper, we show the global existence of the classical solutions to the Boussinesq equations with fractional diffusion by using energy methods, the Fourier localization technique, and Bony's paraproduct decomposition.

We establish the local well-posedness and obtain a blow-up criterion of smooth solutions for the Boussinesq equations in the framework of Triebel-Lizorkin-Lorentz spaces. The main ingredients of our proofs are Littlewood-Paley decomposition and the paradifferential calculus.

We study the finite time blow up of smooth solutions to the Compressible Navier-Stokes system when the initial data contain vacuums. We prove that any classical solutions of viscous compressible fluids without heat conduction will blow up in finite time, as long as the initial data has an isolated mass group (see definition in the paper). The resul...

In this paper, we establish the local well-posedness for the quasi-geostrophic equations and obtain a blow-up criterion of smooth solutions in the framework of Triebel-Lizorkin-Lorentz spaces by adapting a method in Chen-Miao-Zhang (Arch. Rational Mech. Anal. 195: 2010, 561–578). Our new function spaces contain the classical Triebel-Lizorkin spaces...

In this paper, we study the global subsonic irrotational flows in a multi-dimensional ($n\geq 2$) infinitely long nozzle with variable cross sections. The flow is described by the inviscid potential equation, which is a second order quasilinear elliptic equation when the flow is subsonic. First, we prove the existence of the global uniformly subson...

In this paper, the behavior of shock-capturing methods in Lagrangian coordinate is investigated. The relation between viscous shock and inviscid one is analyzed quantitatively, and the procedure of a viscous shock formation and propagation with a jump type initial data is described. In general, a viscous shock profile and a discontinuous one includ...

In this paper, we study the well-posedness problem on transonic shocks for steady ideal compressible flows through a two-dimensional slowly varying nozzle with an appropriately given pressure at the exit of the nozzle. This is motivated by the following transonic phenomena in a de Laval nozzle. Given an appropriately large receiver pressure P r ,...

The upwind discontinuous Galerkin methods with triangle meshes for two dimensional neutron transport equations is studied. The stability for the semi-discrete and full-discrete methods is proved.

In the book [8] of Courant and Friedrichs, the following transonic phenomena in a nozzle is illustrated: Given the appropriately large receiver pressure p r , if the upstream flow is still supersonic behind the throat of the nozzle, then at a certain place in the diverging part of the nozzle a shock front intervenes and the gas is compressed and sl...