The paper reports a multiple source modeling of low-Reynolds-number dissipation rate equation with aids of DNS data. The key features of the model are to satisfy the wall limiting conditions of the individual source terms in the exact dissipation rate equation using the wall damping functions. The wall damping functions are formulated in term of dimensionless dissipation length scale ι(sup)+(sub)D(≡ι(sub)D($upsilon$$xi$)(sup)1/4/$upsilon$) and the invariants of small and large scale turbulence anisotropy tensors. $alpha$(sub)ij(=$mu$(sub)i$mu$(sub)j/$kappa$-2$delta$(sub)ij/3) and e(sub)ij(=$xi$(sub)ij/$xi$-2$delta$(sub)ij/3). The model constants are optimized with aids of DNS data in a plane channel flow. Adopting the dissipation length scale as a parameter of damping function, the applicabilities of $kappa$-$xi$ model are extended to the turbulent flow calculation of complex flow passages.