1,296 research outputs found
Low-diffusivity scalar transport using a WENO scheme and dual meshing
Interfacial mass transfer of low-diffusive substances in an unsteady flow
environment is marked by a very thin boundary layer at the interface and other
regions with steep concentration gradients. A numerical scheme capable of
resolving accurately most details of this process is presented. In this scheme,
the fourth-order accurate WENO method developed by Liu et al. (1994) was
implemented on a non-uniform staggered mesh to discretize the scalar convection
while for the scalar diffusion a fourth-order accurate central discretization
was employed. The discretization of the scalar convection-diffusion equation
was combined with a fourth-order Navier-Stokes solver which solves the
incompressible flow. A dual meshing strategy was employed, in which the scalar
was solved on a finer mesh than the incompressible flow. The solver was tested
by performing a number of two-dimensional simulations of an unstably stratified
flow with low diffusivity scalar transport. The unstable stratification led to
buoyant convection which was modelled using a Boussinesq approximation with a
linear relationship between flow temperature and density. The order of accuracy
for one-dimensional scalar transport on a stretched and uniform grid was also
tested. The results show that for the method presented above a relatively
coarse mesh is sufficient to accurately describe the fluid flow, while the use
of a refined mesh for the low-diffusive scalars is found to be beneficial in
order to obtain a highly accurate resolution with negligible numerical
diffusion
A comparative study of the efficiency of jet schemes
We present two versions of third order accurate jet schemes, which achieve
high order accuracy by tracking derivative information of the solution along
characteristic curves. For a benchmark linear advection problem, the efficiency
of jet schemes is compared with WENO and Discontinuous Galerkin methods of the
same order. Moreover, the performance of various schemes in tracking solution
contours is investigated. It is demonstrated that jet schemes possess the
simplicity and speed of WENO schemes, while showing several of the advantages
as well as the accuracy of DG methods.Comment: 12 pages, 6 figures, presented at the conference Mathematical
Modeling and Applications to Industrial Problems 201
A Compact Third-order Gas-kinetic Scheme for Compressible Euler and Navier-Stokes Equations
In this paper, a compact third-order gas-kinetic scheme is proposed for the
compressible Euler and Navier-Stokes equations. The main reason for the
feasibility to develop such a high-order scheme with compact stencil, which
involves only neighboring cells, is due to the use of a high-order gas
evolution model. Besides the evaluation of the time-dependent flux function
across a cell interface, the high-order gas evolution model also provides an
accurate time-dependent solution of the flow variables at a cell interface.
Therefore, the current scheme not only updates the cell averaged conservative
flow variables inside each control volume, but also tracks the flow variables
at the cell interface at the next time level. As a result, with both cell
averaged and cell interface values the high-order reconstruction in the current
scheme can be done compactly. Different from using a weak formulation for
high-order accuracy in the Discontinuous Galerkin (DG) method, the current
scheme is based on the strong solution, where the flow evolution starting from
a piecewise discontinuous high-order initial data is precisely followed. The
cell interface time-dependent flow variables can be used for the initial data
reconstruction at the beginning of next time step. Even with compact stencil,
the current scheme has third-order accuracy in the smooth flow regions, and has
favorable shock capturing property in the discontinuous regions. Many test
cases are used to validate the current scheme. In comparison with many other
high-order schemes, the current method avoids the use of Gaussian points for
the flux evaluation along the cell interface and the multi-stage Runge-Kutta
time stepping technique.Comment: 27 pages, 38 figure
A low-numerical dissipation, patch-based adaptive-mesh-refinement method for large-eddy simulation of compressible flows
This paper describes a hybrid finite-difference method for the large-eddy simulation of compressible flows with low-numerical dissipation and structured adaptive mesh refinement (SAMR). A conservative flux-based approach is described with an explicit centered scheme used in turbulent flow regions while a weighted essentially non-oscillatory (WENO) scheme is employed to capture shocks. Three-dimensional numerical simulations of a Richtmyer-Meshkov instability are presented
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