A regularised one-dimensional drop formation and coalescence model using a total variation diminishing (TVD) scheme on a single Eulerian grid

Total variation diminishing (TVD) schemes have been recently introduced for the calculation of the one-dimensional unsteady flow in the inlet and outlet pipes of internal combustion engines. This paper describes the flux difference splitting technique (with first- or second-order upwind fluxes) for the classic TVD schemes. To avoid problems at nodes with a section change, a new TVD scheme is developed. This paper further describes a method to impose the boundary condition at the pipe end, independent of the numerical scheme used. This is shown for a reservoir inlet of the pipe and a subsonic outlet flow. For two test cases (the shock-tube and the tapered-pipe calculation), the new TVD algorithm is compared with the classic TVD schemes. The evaluation shows that the new cell—vertex TVD scheme with superbee limiter in two stage form combines a high accuracy with an exact representation of the mass flow in each of the nodes.

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Application of Total Variation Diminishing for 1D Nozzle Problem

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.393.872 ◽

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.

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

Journal of Computational Engineering ◽

10.1155/2015/575380 ◽

2015 ◽

Vol 2015 ◽

pp. 1-10 ◽

Cited By ~ 2

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.

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