Abstract: This work is aimed at developing front tracking methods based on conservation properties of ows for the one and two dimensional Euler systems of uid dynamics. The main idea of the work, which distinguishs the present methods from the traditioanl front tracking methods, is that they track discontinuities by enforcing the conservation properties in the numerical solutions. In doing this way, robustness are expected to be archieved for these tracking methods. Progresses and problems in this developement are discussed. Finally, numerical examples are presented to show the excellency of the methods. Key-Words: front tracking, robustness, enforcing conservation properties, cell-average, discontinuity interaction. The PDE's under concern are Euler systems of hyperbolic equations in one and two space dimensions. As is well known, these systems describe the ows of nonviscous compressible uid; they embody the conservation of mass, momentum, and total energy. Our work is aimed a
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