Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws

An accurate moving boundary formulation in cut-cell methods

https://www.brown.edu/research/projects/scientific-computing/sites/brown.edu.research.projects.scientific-computing/files/uploads/High%20order%20WENO%20and%20DG%20methods%20for%20time-dependent%20convection-dominated%20PDEs.pdf

High order WENO and DG methods for time-dependent convection-dominated PDEs

Spatial finite-difference (FD) coefficients are usually determined by the Taylor-series expansion (TE) or optimization methods. The former can provide high accuracy on a smaller wavenumber or frequency zone, and the latter can give moderate accuracy on a larger zone. Present optimization methods applied to calculate FD coefficients are generally gradient-like or global optimization-like algorithms, and thus iterations are involved. They are more computationally expensive, and sometimes the global solution may not be found. I examined second-order spatial derivatives and computed the optimized spatial FD coefficients over the given wavenumber range using the least-squares (LS) method. The results indicated that the FD accuracy increased with increasing operator length and decreasing wavenumber range. Therefore, for the given error and operator length, globally optimal spatial FD coefficients can be easily obtained. Some optimal FD coefficients were given. I developed schemes to obtain optimized LS-...

Globally optimal finite-difference schemes based on least squares

The effects of large scale perturbation-generating obstacles on the propagation of detonation filled with methane–oxygen mixture

Inverse Lax-Wendroff procedure for numerical boundary conditions of conservation laws

https://www.brown.edu/research/projects/scientific-computing/sites/brown.edu.research.projects.scientific-computing/files/uploads/Efficient%20implementation%20of%20high%20order.pdf

Efficient implementation of high order inverse Lax-Wendroff boundary treatment for conservation laws

/pdf/an-efficient-finite-difference-method-with-high-order-1asi5uf0hs.pdf

An efficient finite-difference method with high-order accuracy in both time and space domains for modelling scalar-wave propagation

A high order moving boundary treatment for compressible inviscid flows

Directly imaging steeply dipping fault zones is difficult for conventional migration, including reverse-time migration (RTM). We developed a new least-squares RTM (LSRTM) method to directly image steeply dipping fault zones. The method uses a wavefield-separation imaging condition and updated source wavefields during each iteration. Our new imaging method produces horizontal-looking images that show mostly steeply dipping fault zones. Conventional least-squares RTM does not update source wavefields and cannot directly image vertical fault zones. We numerically determined that it is crucial to update source wavefields to image steeply dipping fault zones. Using synthetic seismic data, we proved that our new LSRTM method can directly image steeply dipping fault zones with dipping angles up to 90°. Compared with conventional LSRTM, our LSRTM method was less sensitive to the smoothness and the velocity error of the initial migration velocity model.

Sirui Tan

Papers

Inverse Lax-Wendroff procedure for numerical boundary conditions of conservation laws

Efficient implementation of high order inverse Lax-Wendroff boundary treatment for conservation laws

An efficient finite-difference method with high-order accuracy in both time and space domains for modelling scalar-wave propagation

A high order moving boundary treatment for compressible inviscid flows

Least-squares reverse-time migration with a wavefield-separation imaging condition and updated source wavefields