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 new total variation diminishing scheme for the calculation of one-dimensional flow in inlet and exhaust pipes of internal combustion engines

1998 ◽  
Vol 212 (5) ◽  
pp. 437-448 ◽  
Author(s):  
M Vandevoorde ◽  
J Vierendeels ◽  
E Dick ◽  
R Sierens
Keyword(s):  
Total Variation ◽  
Internal Combustion Engines ◽  
Internal Combustion ◽  
Tvd Scheme ◽  
Combustion Engines ◽  
Tvd Schemes ◽  
Total Variation Diminishing ◽  
One Dimensional ◽  
Splitting Technique ◽  
Variation Diminishing

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.

Sign in / Sign up

Export Citation Format

Share Document