scholarly journals Improving Accuracy of the Fifth-Order WENO Scheme by Using the Exponential Approximation Space

2021 ◽  
Vol 59 (1) ◽  
pp. 143-172
Author(s):  
Youngsoo Ha ◽  
Chang Ho Kim ◽  
Hyoseon Yang ◽  
Jungho Yoon
Keyword(s):  
Weno Scheme ◽  
Exponential Approximation ◽  
Approximation Space ◽  
Improving Accuracy ◽  
Fifth Order

An Improved Hybrid Alternative WENO Scheme for High Mach Number Flows

2021 ◽  
Author(s):  
Uttam Singh Rajput ◽  
Krishna Mohan Singh
Keyword(s):  
High Speed ◽  
Compressible Flows ◽  
Weno Scheme ◽  
Test Cases ◽  
Present Scheme ◽  
Low Dissipation ◽  
Scale Structures ◽  
High Mach ◽  
Fifth Order ◽  
High Resolution Method

Abstract This study presents the development of a fifth-order hybrid alternative mapped weighted essentially non-oscillatory scheme (HAW-M) for high-speed compressible flows. A new, improved smoothness indicator has been developed to design the HAW-M scheme. The performance of the present scheme has been evaluated through different one and two-dimensional test cases. The developed scheme shows higher accuracy and low dissipation. Further, it captures the fine-scale structures smoothly than the existing high-resolution method.

scholarly journals NUMERICAL SIMULATION OF THREE-DIMENSIONAL FLOW AROUND HARBOR DUE TO TSUNAMI USING FAVOR METHOD AND WENO SCHEME

2018 ◽  
pp. 71
Author(s):  
Yuki Kajikawa ◽  
Masamitsu Kuroiwa ◽  
Naohiro Otani
Keyword(s):  
Flow Field ◽  
Large Scale ◽  
Three Dimensional ◽  
Weno Scheme ◽  
Scale Model ◽  
Governing Equations ◽  
3D Flow ◽  
Complex Boundaries ◽  
Cartesian Coordinate ◽  
Fifth Order

In this paper, a three-dimensional (3D) tsunami flow model was proposed in order to predict a 3D flow field around a harbor accurately when tsunami strikes. In the proposed numerical model, the Cartesian coordinate system was adopted, and the Fractional Area/Volume Obstacle Representation (FAVOR) method, which has the ability to impose boundary conditions smoothly at complex boundaries, was introduced into the governing equations in consideration of applying the estimation to actual harbors with complex shape in the future. Moreover, the fifth-order Weighted Essentially Non- Oscillatory (WENO) scheme, which is a technique for achieving high accuracy even if the calculation mesh is coarse, was applied to discretization of the convection terms of the governing equations. In order to verify the validity of the model, it was applied to a large-scale laboratory experiment with a scale model of harbor. Comparisons between the simulated and experimental results showed that the model was able to reproduce the time variation of the flow field with sufficient accuracy. Moreover, the simulated results showed that a complex 3D flow field with some vertical vortex flows was generated around a harbor when tsunami struck.

scholarly journals The accuracy of finite-difference schemes calculating the interaction of shock waves

2019 ◽  
Vol 485 (6) ◽  
pp. 691-696 ◽  
Author(s):  
V. V. Ostapenko ◽  
N. A. Khandeeva
Keyword(s):  
Finite Difference ◽  
Shock Waves ◽  
Difference Schemes ◽  
Weno Scheme ◽  
Shock Capturing ◽  
Finite Difference Schemes ◽  
Third Order ◽  
Interaction Of Shock Waves ◽  
Fifth Order

The accuracy with which the shock-capturing finite-difference schemes calculate the flows with interaction of shock waves is studied. It is shown that, in the domains between the shock waves after their incidence, the calculation accuracy of invariants of the combined schemes is several orders of magnitude higher than the accuracy of the WENO-scheme, which is fifth-order in space and third-order in time.

scholarly journals A high performance fifth‐order multistep WENO scheme

2019 ◽  
Vol 91 (4) ◽  
pp. 159-182 ◽  
Author(s):  
Fangjun Zeng ◽  
Yiqing Shen ◽  
Shengping Liu ◽  
Li Liu
Keyword(s):  
High Performance ◽  
Weno Scheme ◽  
Fifth Order

Delayed Detached Eddy Simulation of Airfoil Stall Flows Using High-Order Schemes

2014 ◽  
Vol 136 (11) ◽  
Author(s):  
Hong-Sik Im ◽  
Ge-Cheng Zha
Keyword(s):  
Second Order ◽  
High Order ◽  
Weno Scheme ◽  
Navier Stokes ◽  
Detached Eddy Simulation ◽  
High Order Scheme ◽  
Eddy Simulation ◽  
Naca0012 Airfoil ◽  
Order Scheme ◽  
Fifth Order

An advanced hybrid Reynolds-Averaged Navier–Stokes/large eddy simulation (RANS/LES) turbulence model delayed detached eddy simulation (DDES) is conducted in thispaper to investigate the dynamic stall flows over 3D NACA0012 airfoil at 17 deg, 26 deg, 45 deg, and 60 deg angle of attack (AOA). The spatially filtered unsteady 3D Navier–Stokes equations are solved using a fifth-order weighted essentially nonoscillatory (WENO) reconstruction with a low diffusion E-CUSP (LDE) scheme for the inviscid fluxes and a conservative fourth-order central differencing for the viscous terms. An implicit second-order time marching scheme with dual time stepping is employed to achieve high stability and convergency rate. A 3D flat plate is validated for the DDES model. For quantitative prediction of lift and drag of the stalled NACA0012 airfoil flows, the detached eddy simulation (DES) and DDES achieve much more accurate results than the Unsteady Reynolds-Averaged Navier–Stokes (URANS) simulation. In addition to the quantitative difference, the DES/DDES and URANS also obtain qualitatively very different unsteady stalled flows of NACA0012 airfoil with different vortical structures and frequencies. This may bring a significantly different prediction if those methods are used for fluid–structural interaction. For comparison purpose, a third-order WENO scheme with a second-order central differencing is also employed for the DDES stalled NACA0012 airfoil flows. Both the third- and fifth-order WENO schemes predict the stalled flow similarly for lift and drag at AOA less than 45 deg, while at AOA of 60 deg, the fifth-order WENO scheme shows better agreement with the experiment than the third-order WENO scheme. The high-order scheme of WENO 5 also resolves more small scales of flow structures than the second-order scheme. The prediction of the stalled airfoil flow using DDES with both the high-order scheme and second-order scheme is overall significantly more accurate than the URANS simulation.

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