A Hybrid, Explicit-Implicit, Second Order in Space and Time TVD scheme for One-Dimensional Scalar Conservation Laws

2011 ◽  
Author(s):  
Farhang Norouzi ◽  
Eugene Timofeev
Keyword(s):  
Conservation Laws ◽  
Second Order ◽  
Tvd Scheme ◽  
Scalar Conservation Laws ◽  
One Dimensional ◽  
Space And Time ◽  
Scalar Conservation

BEHAVIOR OF TVD LIMITERS ON THE SOLUTION OF NON-LINEAR HYPERBOLIC EQUATION

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1507-1510
Author(s):  
K. R. QURESHI ◽  
C-H. LEE
Keyword(s):  
Burger Equation ◽  
Second Order ◽  
Tvd Scheme ◽  
Scalar Conservation Laws ◽  
Linear Hyperbolic Equation ◽  
One Dimensional ◽  
Non Linear ◽  
Spurious Oscillations ◽  
Explicit Finite Difference ◽  
Scalar Conservation

The main objective of the present work is to solve the non-linear inviscid Burger equation using the second-order TVD scheme with the different TVD limiters. These limiters include Non-MUSCL (monotone upwind scalar conservation laws) Harten-Yee upwind limiters, Roe-Sweby upwind limiters and Davis-Yee symmetric TVD limiters. These limiters are then used in conjunction with the explicit finite difference second order TVD scheme to model the flow in which discontinuity is present. Non-linear Burger equation was solved for this purpose to capture a one dimensional traveling discontinuity. Every limiter was individually tested for its ability to resolve the discontinuity in as few mesh point as possible. In addition, each limiter's capability to eliminate spurious oscillations associated with numerical computation of discontinuities was investigated. The results showed that all the TVD limiters were able to completely eliminate the spurious oscillations except Roe-Sweby limiter that caused the solution to diverge.

One-Dimensional Scalar Conservation Laws with Regulated Data

2020 ◽  
Vol 52 (3) ◽  
pp. 3114-3130
Author(s):  
Helge Kristian Jenssen ◽  
Johanna Ridder
Keyword(s):  
Conservation Laws ◽  
Scalar Conservation Laws ◽  
One Dimensional ◽  
Scalar Conservation

scholarly journals Fractional BV spaces and applications to scalar conservation laws

2014 ◽  
Vol 11 (04) ◽  
pp. 655-677 ◽  
Author(s):  
C. Bourdarias ◽  
M. Gisclon ◽  
S. Junca
Keyword(s):  
Conservation Laws ◽  
Stability Result ◽  
Entropy Solutions ◽  
Smoothing Effect ◽  
Scalar Conservation Laws ◽  
One Dimensional ◽  
Regular Functions ◽  
Bv Functions ◽  
Scalar Conservation ◽  
First Time

We obtain new fine properties of entropy solutions to scalar nonlinear conservation laws. For this purpose, we study the "fractional BV spaces" denoted by BVs(ℝ) (for 0 < s ≤ 1), which were introduced by Love and Young in 1937 and closely related to the critical Sobolev space Ws,1/s(ℝ). We investigate these spaces in connection with one-dimensional scalar conservation laws. The BVs spaces allow one to work with less regular functions than BV functions and appear to be more natural in this context. We obtain a stability result for entropy solutions with BVs initial data. Furthermore, for the first time, we get the maximal Ws,p smoothing effect conjectured by Lions, Perthame and Tadmor for all nonlinear (possibly degenerate) convex fluxes.

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