1,176 research outputs found
A modified fifth-order WENO scheme for hyperbolic conservation laws
This paper deals with a new fifth-order weighted essentially non-oscillatory
(WENO) scheme improving the WENO-NS and WENO-P methods which are introduced in
Ha et al. J. Comput. Phys. (2013) and Kim et al., J. Sci. Comput. (2016)
respectively. These two schemes provide the fifth-order accuracy at the
critical points where the first derivatives vanish but the second derivatives
are non-zero. In this paper, we have presented a scheme by defining a new
global-smoothness indicator which shows an improved behavior over the solution
to the WENO-NS and WENO-P schemes and the proposed scheme attains optimal
approximation order, even at the critical points where the first and second
derivatives vanish but the third derivatives are non-zero.Comment: 23 pages, 14 figure
An Adaptive Characteristic-wise Reconstruction WENOZ scheme for Gas Dynamic Euler Equations
Due to its excellent shock-capturing capability and high resolution, the WENO
scheme family has been widely used in varieties of compressive flow simulation.
However, for problems containing strong shocks and contact discontinuities,
such as the Lax shock tube problem, the WENO scheme still produces numerical
oscillations. To avoid such numerical oscillations, the characteristic-wise
construction method should be applied. Compared to component-wise
reconstruction, characteristic-wise reconstruction leads to much more
computational cost and thus is not suite for large scale simulation such as
direct numeric simulation of turbulence. In this paper, an adaptive
characteristic-wise reconstruction WENO scheme, i.e. the AdaWENO scheme, is
proposed to improve the computational efficiency of the characteristic-wise
reconstruction method. The new scheme performs characteristic-wise
reconstruction near discontinuities while switching to component-wise
reconstruction for smooth regions. Meanwhile, a new calculation strategy for
the WENO smoothness indicators is implemented to reduce over-all computational
cost. Several one dimensional and two dimensional numerical tests are performed
to validate and evaluate the AdaWENO scheme. Numerical results show that
AdaWENO maintains essentially non-oscillatory flow field near discontinuities
as the characteristic-wise reconstruction method. Besieds, compared to the
component-wise reconstruction, AdaWENO is about 40\% faster which indicates its
excellent efficiency
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
New Constructing Method for WENO Schemes
AbstractA new method for constructing weighted essentially non-oscillatory (WENO) scheme is proposed. The idea of this method is to combine Henrick's mapping function and the idea of improving the accuracy of WENO-Z scheme one-by-one order. The particular advantage of the new constructing method is that it can improve the accuracy of WENO scheme near discontinuities. Numerical examples show that the new constructing method is very efficient and robust, and the new WENO scheme is more accurate than the original ones
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