A New TVD Scheme for Gradient Smoothing Method Using Unstructured Grids

2019 ◽  
Vol 17 (03) ◽  
pp. 1850132 ◽  
Author(s):  
Guiyong Zhang ◽  
Da Hui ◽  
Da Li ◽  
Li Zou ◽  
Shengchao Jiang ◽  
...  
Keyword(s):  
Unstructured Meshes ◽  
Smoothing Method ◽  
Tvd Scheme ◽  
Hyperbolic Partial Differential Equation ◽  
Variation Diminishing ◽  
Structured Meshes ◽  
Gradient Smoothing ◽  
Discontinuous Problems ◽  
Flux Limiters ◽  
Present Algorithm

An improved [Formula: see text]-factor algorithm for implementing total variation diminishing (TVD) scheme has been proposed for the gradient smoothing method (GSM) using unstructured meshes. Different from the methods using structured meshes, for the methods using unstructured meshes, generally the upwind point cannot be clearly defined. In the present algorithm, the value of upwind point has been successfully approximated for unstructured meshes by using the GSM with different gradient smoothing schemes, including node GSM (nGSM) midpoint GSM (mGSM) and centroid GSM (cGSM). The present method has been used to solve hyperbolic partial differential equation discontinuous problems, where three classical flux limiters (Superbee, Van leer and Minmod) were used. Numerical results indicate that the proposed algorithm based on mGSM and cGSM schemes can avoid the numerical oscillation and reduce the numerical diffusion effectively. Generally the scheme based on cGSM leads to the best performance among the three proposed schemes in terms of accuracy and monotonicity.

Application of Total Variation Diminishing for 1D Nozzle Problem

2013 ◽  
Vol 393 ◽  
pp. 872-877
Author(s):  
Fatimah Yusop ◽  
Bambang Basuno ◽  
Zamri Omar
Keyword(s):  
Differential Equation ◽  
Fluid Dynamics ◽  
Partial Differential Equation ◽  
Total Variation ◽  
Tvd Scheme ◽  
Total Variation Diminishing ◽  
Variation Diminishing ◽  
Computational Fluid Dynamics Cfd ◽  
Runge Kutta ◽  
Central Scheme

Computational fluid dynamics (CFD) is very widespread use every day as a tool in fluid flow analyses. In order to solve the Partial Differential Equation (PDE), there are few approach been introduced. The total variation diminishing (TVD) is a most popular scheme which is usually used in combination with other scheme. Therefore, this study develops CFD code by using Runge-Kutta which based on combination of central scheme and TVD scheme. Comparison was done through purely Runge-Kutta and after implemented TVD. The result shows that combination of Runge-Kutta and TVD approach are more stable as compared to purely Runge-Kutta approach.

A Novel Alpha Gradient Smoothing Method (αGSM) for Fluid Problems

2012 ◽  
Vol 61 (3) ◽  
pp. 204-228 ◽  
Author(s):  
Eric Li ◽  
Vincent Tan ◽  
George X. Xu ◽  
G. R. Liu ◽  
Z. C. He
Keyword(s):  
Smoothing Method ◽  
Gradient Smoothing

Numerical Simulation of Vortex Shedding and Lock-in Characteristics for a Thin Cambered Blade

2007 ◽  
Vol 129 (10) ◽  
pp. 1297-1305 ◽  
Author(s):  
Baoshan Zhu ◽  
Jun Lei ◽  
Shuliang Cao
Keyword(s):  
Numerical Simulation ◽  
Vortex Shedding ◽  
Forced Oscillation ◽  
Tvd Scheme ◽  
Convective Term ◽  
Variation Diminishing ◽  
Vortex Shedding Frequency ◽  
Shedding Frequency ◽  
Lock In ◽  
Phase Differences

In this paper, vortex-shedding patterns and lock-in characteristics that vortex-shedding frequency synchronizes with the natural frequency of a thin cambered blade were numerically investigated. The numerical simulation was based on solving the vorticity-stream function equations with the fourth-order Runge–Kutta scheme in time and the Chakravaythy–Oscher total variation diminishing (TVD) scheme was used to discretize the convective term. The vortex-shedding patterns for different blade attack angles were simulated. In order to confirm whether the vortex shedding would induce blade self-oscillation, numerical simulation was also carried out for blade in a forced oscillation. By changing the pitching frequency and amplitude, the occurrence of lock-in at certain attack angles was determined. Inside the lock-in zone, phase differences between the blade’s pitching displacement and the torque acting on the blade were used to infer the probability of the blade self-oscillation.

scholarly journals Development of High-Resolution Total Variation Diminishing Scheme for Linear Hyperbolic Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Rabie A. Abu Saleem ◽  
Tomasz Kozlowski
Keyword(s):  
High Resolution ◽  
Total Variation ◽  
Initial Conditions ◽  
Hyperbolic Problems ◽  
Total Variation Diminishing ◽  
One Dimensional ◽  
Flux Limiter ◽  
Variation Diminishing ◽  
Flux Limiters ◽  
Theta Method

A high-resolution, total variation diminishing (TVD) stable scheme is derived for scalar hyperbolic problems using the method of flux limiters. The scheme was constructed by combining the 1st-order upwind scheme and the 3rd-order quadratic upstream interpolation scheme (QUICK) using new flux limiter function. The new flux limiter function was established by imposing several conditions to ensure the TVD properties of the scheme. For temporal discretization, the theta method was used, and values for the parameter θ were chosen such that the scheme is unconditionally stable. Numerical results are presented for one-dimensional pure advection problems with smooth and discontinuous initial conditions and are compared to those of other known numerical schemes. The results show that the proposed numerical method is stable and of higher order than other common schemes.

A local gradient smoothing method for solving strong form governing equation

2020 ◽  
Vol 84 ◽  
pp. 104073
Author(s):  
Songhun Kwak ◽  
Kwanghun Kim ◽  
Kwangnam Choe ◽  
Kumchol Yun
Keyword(s):  
Governing Equation ◽  
Smoothing Method ◽  
Strong Form ◽  
Gradient Smoothing ◽  
Local Gradient
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