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We develop high order discontinuous Galerkin (DG) methods with Lax-Friedrich fluxes for Euler equations under gravitational fields. Such problems may yield steady-state solutions and the density and p...
Whether the 3D incompressible Euler equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In this talk, we will present a ...
The authors recently identified an infinite range of high-order energy stable flux reconstruction (FR) schemes in 1D and on triangular elements in 2D. The new flux reconstructi...
In this paper, we present a mesh-free, finite-volume-like scheme designed for numerically solving conservation laws. We rst derive a conservative formulation for computing mesh-free @...
Higher order discretization has not been widely successful in industrial applications to compressible flow simulation. Among several reasons for this, one may identify the lack of tailor-suited,...
An efficient, high-order, conservative method named the spectral difference method has been developed recently for conservation laws on unstructured grids. It combines the best features of struc...
New versions of implicit algorithms are proposed for the efficient solution of the Euler equations of com pressible flow. The methods are based on a pre conditioned, Lower-Upper (LU) implem...
Starting from the gas-kinetic model, a new class of relaxation schemes for the Euler equations are presented. Instead of linerizing the Euler equa-tions into a few simple waves, the new flow solvers a...
The flow pattern inside an impeller should be determined for maximum eciency and performance. The e ects of the design parameters on the pump performance can be determined using numerical calculation...

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