This paper establishes the resolution finite volume scheme with slope entropy convergence of a new two-value high relaxation for conservation laws. This scheme, motivated by the general method of high resolution schem...This paper establishes the resolution finite volume scheme with slope entropy convergence of a new two-value high relaxation for conservation laws. This scheme, motivated by the general method of high resolution schemes that have high-order accuracy in smooth regions of solutions and are free of oscillations near discontinuities, unifies and evolves slopes directly with a slope relaxation equation that governs the evolution of slopes in both smooth and discontinuous regions. Proper choices of slopes are realized adaptively via a relaxation parameter. The scheme is shown to be total-variation-bounded （TVB） stable and satisfies cell-entropy inequalities.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11371063,11501040,and 91530108)the Doctoral Program from the Education Ministry of China(No.20130003110004)
文摘This paper establishes the resolution finite volume scheme with slope entropy convergence of a new two-value high relaxation for conservation laws. This scheme, motivated by the general method of high resolution schemes that have high-order accuracy in smooth regions of solutions and are free of oscillations near discontinuities, unifies and evolves slopes directly with a slope relaxation equation that governs the evolution of slopes in both smooth and discontinuous regions. Proper choices of slopes are realized adaptively via a relaxation parameter. The scheme is shown to be total-variation-bounded （TVB） stable and satisfies cell-entropy inequalities.
