We present a newly developed cosmological hydrodynamics code based on weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation laws. WENO is a higher order accurate finite difference scheme designed for problems with piecewise smooth solutions containing discontinuities, and has been successfully applied for problems involving both shocks and complicated smooth solution structures. We couple hydrodynamics based on the WENO scheme with standard Poisson solver - particle-mesh (PM) algorithm for evolving the self-gravitating system. The third order low storage total variation diminishing (TVD) Runge-Kutta scheme has been used for the time integration of the system. To test accuracy and convergence rate of the code, we subject it to a number of typical tests including the Sod shock tube in multidimensions, the Sedov blast wave and formation of the Zeldovich pancake. These tests validate the WENO hydrodynamics with fast convergence rate and high accuracy. We also evolve a low density flat cosmological model ($Lambda$CDM) to explore the validity of the code in practical simulations.
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