Analyzing advantages and disadvantages of three Riemann solvers of AC(Acoustic), MFCAV(Multi Fluid Channel on Averaged Volume) and HLLC for compressible multimaiterial fluid problems, we constructed an adaptive Riemann solver(ADRS) as a weighted average of three solvers. Rule for designing weights is discussed in detail. ADRS Riemann solver is applied to a compatible cell-centered Lagrangian method which resisting spurious mesh deformation by viewing MFCAV as a modification of AC solver. Numerical examples include Taylor Green vortex problem are given to show efficiency of the method.