scholarly journals An adaptive multilevel wavelet framework for scale-selective WENO reconstruction schemes

2018 ◽  
Vol 87 (5) ◽  
pp. 239-269 ◽  
Author(s):  
R. Maulik ◽  
O. San ◽  
R. Behera
Keyword(s):  
Weno Reconstruction

Adaptive ADER Methods Using Kernel-Based Polyharmonic Spline WENO Reconstruction

2010 ◽  
Vol 32 (6) ◽  
pp. 3251-3277 ◽  
Author(s):  
Terhemen Aboiyar ◽  
Emmanuil H. Georgoulis ◽  
Armin Iske
Keyword(s):  
Weno Reconstruction ◽  
Polyharmonic Spline ◽  
Ader Methods

scholarly journals A Slope Constrained 4th Order Multi-Moment Finite Volume Method with WENO Limiter

2015 ◽  
Vol 18 (4) ◽  
pp. 901-930 ◽  
Author(s):  
Ziyao Sun ◽  
Honghui Teng ◽  
Feng Xiao
Keyword(s):  
Conservation Laws ◽  
Finite Volume ◽  
Solution Structure ◽  
Hyperbolic Conservation Laws ◽  
High Order ◽  
Weno Reconstruction ◽  
Hyperbolic Conservation ◽  
Average Value ◽  
High Order Schemes ◽  
Volume Method

AbstractThis paper presents a new and better suited formulation to implement the limiting projection to high-order schemes that make use of high-order local reconstructions for hyperbolic conservation laws. The scheme, so-called MCV-WENO4 (multi-moment Constrained finite Volume with WENO limiter of 4th order) method, is an extension of the MCV method of Ii & Xiao (2009) by adding the 1st order derivative (gradient or slope) at the cell center as an additional constraint for the cell-wise local reconstruction. The gradient is computed from a limiting projection using the WENO (weighted essentially non-oscillatory) reconstruction that is built from the nodal values at 5 solution points within 3 neighboring cells. Different from other existing methods where only the cell-average value is used in the WENO reconstruction, the present method takes account of the solution structure within each mesh cell, and thus minimizes the stencil for reconstruction. The resulting scheme has 4th-order accuracy and is of significant advantage in algorithmic simplicity and computational efficiency. Numerical results of one and two dimensional benchmark tests for scalar and Euler conservation laws are shown to verify the accuracy and oscillation-less property of the scheme.

Comparison of Fifth-Order WENO Scheme and Finite Volume WENO-Gas-Kinetic Scheme for Inviscid and Viscous Flow Simulation

2013 ◽  
Vol 14 (3) ◽  
pp. 599-620 ◽  
Author(s):  
Jun Luo ◽  
Lijun Xuan ◽  
Kun Xu
Keyword(s):  
Finite Volume ◽  
Control Volume ◽  
High Order ◽  
Gas Evolution ◽  
Weno Reconstruction ◽  
Flux Function ◽  
High Order Schemes ◽  
Order Reconstruction ◽  
High Order Reconstruction ◽  
Fifth Order

AbstractThe development of high-order schemes has been mostly concentrated on the limiters and high-order reconstruction techniques. In this paper, the effect of the flux functions on the performance of high-order schemes will be studied. Based on the same WENO reconstruction, two schemes with different flux functions, i.e., the fifth-order WENO method and the WENO-Gas-kinetic scheme (WENO-GKS), will be compared. The fifth-order finite difference WENO-SW scheme is a characteristic variable reconstruction based method which uses the Steger-Warming flux splitting for inviscid terms, the sixth-order central difference for viscous terms, and three stages Runge-Kutta time stepping for the time integration. On the other hand, the finite volume WENO-GKS is a conservative variable reconstruction based method with the same WENO reconstruction. But, it evaluates a time dependent gas distribution function along a cell interface, and updates the flow variables inside each control volume by integrating the flux function along the boundary of the control volume in both space and time. In order to validate the robustness and accuracy of the schemes, both methods are tested under a wide range of flow conditions: vortex propagation, Mach 3 step problem, and the cavity flow at Reynolds number 3200. Our study shows that both WENO-SW and WENO-GKS yield quantitatively similar results and agree with each other very well provided a sufficient grid resolution is used. With the reduction of mesh points, the WENO-GKS behaves to have less numerical dissipation and present more accurate solutions than those from the WENO-SW in all test cases. For the Navier-Stokes equations, since the WENO-GKS couples inviscid and viscous terms in a single flux evaluation, and the WENO-SW uses an operator splitting technique, it appears that the WENO-SW is more sensitive to the WENO reconstruction and boundary treatment. In terms of efficiency, the finite volume WENO-GKS is about 4 times slower than the finite differenceWENO-SW in two dimensional simulations. The current study clearly shows that besides high-order reconstruction, an accurate gas evolution model or flux function in a high-order scheme is also important in the capturing of physical solutions. In a physical flow, the transport, stress deformation, heat conduction, and viscous heating are all coupled in a single gas evolution process. Therefore, it is preferred to develop such a scheme with multi-dimensionality, and unified treatment of inviscid and dissipative terms. A high-order scheme does prefer a high-order gas evolution model. Even with the rapid advances of high-order reconstruction techniques, the first-order dynamics of the Riemann solution becomes the bottleneck for the further development of high-order schemes. In order to avoid the weakness of the low order flux function, the development of high-order schemes relies heavily on the weak solution of the original governing equations for the update of additional degree of freedom, such as the non-conservative gradients of flow variables, which cannot be physically valid in discontinuous regions.

scholarly journals Numerical Approach of the Equilibrium Solutions of a Global Climate Model

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1542
Author(s):  
Arturo Hidalgo ◽  
Lourdes Tello
Keyword(s):  
Numerical Solution ◽  
Climate Model ◽  
Global Climate Model ◽  
Coupled Model ◽  
Deep Ocean ◽  
Stationary Solutions ◽  
Balance Model ◽  
Finite Volume Scheme ◽  
Solar Constant ◽  
Weno Reconstruction

We consider a coupled model surface-deep ocean effect, where an Energy Balance Model (EBM) is used for modelling the surface temperature and a two-dimensional heat equation represents the evolution of the temperature of the deep ocean. Although the model under study is based on that proposed by Watts & Morantine (1990), here we consider a modified model that incorporates other processes, such as the nonlinear diffusion and the action of coalbedo, depending on the temperature. The stationary states of the model under study, taking the solar constant as the parameter, are numerically attained. The results of the simulation are depicted in a {(Q,u)} plot where u is the temperature in the surface and Q is the solar constant. The numerical solution is achieved by means of a finite volume scheme with Weighted Essentially Non-Oscillatory (WENO) reconstruction in space and third order Runge-Kutta scheme, which verifies the Total Variation Diminishing (TVD) property, for time integration. The equilibrium states are accomplished by evolving in time the numerical solution until the stationary solutions are reached. The main novel results of this work concern the numerical obtention of the stationary solutions of both the EBM and the coupled model EBM-deep ocean and the agreement of these results with the theoretically obtained in previous works, where an interval of values of the solar constant Q was obtained with the existence of at least three stationary solutions. In this work, we have numerically obtained more than three stationary solutions for such interval of Q.

An implicit Hermite WENO reconstruction-based discontinuous Galerkin method on tetrahedral grids

2014 ◽  
Vol 96 ◽  
pp. 406-421 ◽  
Author(s):  
Yidong Xia ◽  
Hong Luo ◽  
Robert Nourgaliev
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Weno Reconstruction ◽  
Tetrahedral Grids

scholarly journals Reynolds-Averaged Navier-Stokes Modeling of Turbulent Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz Mixing Using a Higher-Order Shock-Capturing Method

2019 ◽  
Author(s):  
Oleg Schilling
Keyword(s):  
Sulfur Hexafluoride ◽  
Mixing Layer ◽  
Turbulence Models ◽  
Shock Capturing ◽  
Navier Stokes ◽  
Weno Reconstruction ◽  
Third Order ◽  
Central Difference ◽  
Reynolds Averaged Navier Stokes ◽  
Good Agreement

Abstract A numerical implementation of a large number of Reynolds-averaged Navier–Stokes (RANS) models based on two-, three-, four-equation, and Reynolds stress turbulence models (using either the turbulent kinetic energy dissipation rate or the turbulent lengthscale) in an Eulerian, finite-difference shock-capturing code is described. The code uses third-order weighted essentially nonoscillatory (WENO) reconstruction of the advective fluxes, and second- or fourth-order central difference derivatives for the computation of spatial gradients. A third-order TVD Runge–Kutta time-evolution scheme is used to evolve the fields in time. Improved closures for the turbulence production terms, compressibility corrections, mixture transport coefficients, and a consistent initialization methodology for the turbulent fields are briefly summarized. The code framework allows for systematic comparisons of detailed predictions from a variety of turbulence models of increasing complexity. Applications of the code with selected K–ε based models are illustrated for each of the three instabilities. Simulations of Rayleigh–Taylor unstable flows for Atwood numbers 0.1–0.9 are shown to be consistent with previous implicit LES (ILES) results and with the expectation of increased asymmetry in the mixing layer characteristics with increasing stratification. Simulations of reshocked Richtmyer–Meshkov turbulent mixing corresponding to experiments with light-to-heavy transition in air/sulfur hexafluoride and incident shock Mach number Mas = 1.50, and heavy-to-light transition in sulfur hexafluoride/air with Mas = 1.45 are shown to be in generally good agreement with both pre- and post-reshock mixing layer widths. Finally, simulations of the seven Brown–Roshko Kelvin–Helmholtz experiments with various velocity and density ratios using nitrogen, helium, and air are shown to give mixing layer predictions in good agreement with data. The results indicate that the numerical algorithms and turbulence models are suitable for simulating these classes of inhomogeneous turbulent flows.

scholarly journals An incremental-stencil WENO reconstruction for simulation of compressible two-phase flows

2018 ◽  
Vol 104 ◽  
pp. 20-31 ◽  
Author(s):  
Bing Wang ◽  
Gaoming Xiang ◽  
Xiangyu Y. Hu
Keyword(s):  
Two Phase Flows ◽  
Weno Reconstruction ◽  
Two Phase

Evaluation of Riemann flux solvers for WENO reconstruction schemes: Kelvin–Helmholtz instability

2015 ◽  
Vol 117 ◽  
pp. 24-41 ◽  
Author(s):  
Omer San ◽  
Kursat Kara
Keyword(s):  
Helmholtz Instability ◽  
Weno Reconstruction
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