The modified method of characteristics with adjusted advection

The MMOC procedure for approximating the solutions of transport-dominated diiusion problems does not automatically preserve integral conservation laws, leading to (mass) balance errors in many kinds of ow problems. The variant, called the MMOCAA, discussed herein preserves the conservation law at a minor additional computational cost. It is shown that its solution, in either Galerkin or nite diierence form, converges at the same rates as were proved earlier by Douglas and Russell for the standard MMOC procedure.