Constructing exactly conservative scheme in a non-conservative form

A non-conservative scheme that guarantees exact mass conservation is proposed. Although it is in a non-conservative form, the mass of each cell is employed as an additional variable that is advanced in a conservative form. Some numerical tests are carried out to demonstrate the mass conservation and the accurate calculation of the speed of a shock wave even without the viscosity term. © 2000 Elsevier Science B.V. All rights reserved.