Composite High Resolution Localized Relaxation Schemefor Hyperbolic Conservation Laws

Ritesh Kumar DubeyIndian Institute of Information Technology Design & Manufacturing Jabalpur, India

e-mail (riteshkd@iiitdm.in)

Abstarct In this work we extend the high resolution scheme presented in [1] for non-linear problems by usingthe framework of relaxation system that converts a non-linear conservation law into a system of linear convectionequations with non-linear source terms. The characteristic speed of relaxation system is chosen locally on threepoint stencil of grid. This obtained relaxation system is solved using composite schemes technique i.e., usingcombination of proposed scheme with conservative non-standard finite difference scheme. Presented numericalresults show higher resolution near discontinuity without introducing spurious oscillations.

1 Numerical results

1.1 1-D Burgers Equation

Figure 1: Solution profile of 1D-Burgers equation by Composite scheme

References

[1] Kumar R., Kadalbajoo M. K., A High Resolution Total Variation Diminishing Scheme for Hyperbolic Con-servation Law and Related Problems, Applied Mathematics and Computation, 175(2006), 1556-1573.