A recent work of Li et al. [Numer. Math. Theor. Meth. Appl., Vol. 1, pp. 92-112(2008)] proposed a finite volume solver to solve 2D steady Euler equations. Although the Venkatakrishnan limiter is used to prevent the non-physical oscillations nearby the shock region, the overshoot or undershoot phenomenon can still be observed. Moreover, the numerical accuracy is degraded by using Venkatakrishnan...

A discrete-adjoint formulation is presented for the three-dimensional Euler equations discretized on a Cartesian mesh with embedded boundaries. The solution algorithm for the adjoint and flow-sensitivity equations leverages the Runge–Kutta time-marching scheme in conjunction with the parallel multigrid method of the flow solver. The matrix-vector products associated with the linearization of th...

A three-dimensional multi-block Newton-Krylov flow solver for the Euler equations has been developed for steady aerodynamic flows. The solution is computed through a Jacobian-free inexact-Newton method with an approximate-Newton method for startup. The linear system at each outer iteration is solved using a Generalized Minimal Residual (GMRES) Krylov subspace algorithm. An incomplete lower/uppe...

A new high order finite-difference method utilizing the idea of Harten ENO subcell resolution method is proposed for chemical reactive flows and combustion. In reaction problems, when the reaction time scale is very small, e.g., orders of magnitude smaller than the fluid dynamics time scales, the governing equations will become very stiff. Wrong propagation speed of discontinuity may occur due ...

Abstract In this paper, we apply a simple finite element numerical scheme, proposed in an earlier work (Liu in Math Comput 70(234):579–593, 2000), to perform a high resolution numerical simulation of incompressible flow over an irregular domain and analyze its boundary layer separation. Compared with many classical finite element fluid solvers, this numerical method avoids a Stokes solver, and ...

The Time Dependent Boltzmann equation (TDBE) is a viable option to study strongly out-of-equilibrium thermalization dynamics which are becoming increasingly critical for many novel physical applications like Ultrafast thermalization, Terahertz radiation etc. However its applicability greatly limited by the impractical scaling of solution scattering integral term. In our previous work\cite{Micha...

The main objective of the present study is to utilize a novel linearization strategy to linearize the convection terms of the quasi-one-dimensional Euler governing equations on collocated grids and to examine its shock-capturing capabilities. To avoid a pressure checkerboard problem on the collocated grids, it is necessary to utilize two velocity definitions at each cell face. Similarly, we def...

In this paper, we study the convergence analysis for a robust stochastic structure-preserving Lagrangian numerical scheme in computing effective diffusivity of time-dependent chaotic flows, which are modeled by differential equations (SDEs). Our is based on splitting method to solve corresponding SDEs deterministic subproblem discretized using while random Euler-Maruyama scheme. We obtain sharp...