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The phenomenon of dissipation enhancement by transport noise is shown for stochastic 2D Navier–Stokes equations in velocity form. In the 3D case, suppression of blow-up is proved for stochastic Navier...
This paper studies a Cauchy problem for a scalar multidimensional (multi-d) viscous convex conservation law, in which the initial data is a planar viscous shock with a multi-d periodic perturbation. W...
We prove the time-asymptotic stability of composite waves consisting of the superposition of a viscous shock and a rarefaction for the one-dimensional compressible barotropic Navier-Stokes equations. ...
We are concerned with the three-dimensional incompressible Navier–Stokes equations driven by an additive stochastic forcing of trace class. First, for every divergence free initial condition in $L^{2}...
We establish global-in-time existence and non-uniqueness of probabilistically strong solutions to the three dimensional Navier--Stokes system driven by space-time white noise. In this setting, solutio...
This paper presents an adjoint method for the optimum shape design of unsteady three-dimensional viscousflows.The goal is to develop a set of discrete unsteady adjoint equations and the correspo...
This work focuses on the extension of the recently introduced Spectral Difference Method to viscous flow. The spectral difference method is a conservative pseudo-spectral scheme base...
During the last decade, aerodynamic shape optimization methods based on control theory have been intensively developed. The methods have proved to be very e ective for improving wing section shapes fo...
This paper presents an adjoint method for the optimal control of unsteady flows. The goal is to develop the continuous and discrete unsteady adjoint equations and their cor responding boundary c...
This paper follows up on the author’s recent paper “The Construction of Discretely Conservative Finite Volume Schemes that also Globally Conserve Energy or Enthalpy”. In the case of the gas dynamics...
Theoretical developments of flux reconstruction method Unstructured high-order methods The Flux Reconstruction approach Energy Stable Flux Reconstruction schemes Flux Reconstruction as Filtere...
Accordingly, a fast steady state solver is an essential building block for an implicit scheme. This leads to a circular situation. We need an implicit scheme for fast convergence to a steady state, ...
Solution Algorithms for High-Speed Viscous Flows     High-Speed Viscous Flows  aircraft       font style='font-size:12px;'> 2015/6/18
Highly flexible platform for all applied aerodynamics problems and other problems governed by conservation laws • Fast turnaround through convergence acceleration techniques • Framework...
Solution Algorithms for Viscous Flow     Viscous Flow  plane       font style='font-size:12px;'> 2015/6/18
Associate first and second neighbors with each face • Allows implementation of standard schemes with five-point stencils (Jameson-Schmidt-Turkel JST, SLIP) in the same code • Eliminates...
The use of energy estimates to establish the stability of dis crete approximations to initial value problems has a long history. The energy meth od is discussed in the classical book by Morton and...

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