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Abstract: In this paper, we develop a well-balanced oscillation-free discontinuous Galerkin method (OFDG) for the shallow water flow under temperature fields（also called Ripa model）, which can maintain the lake-at-rest steady state. Here, we add an extra damping term to the standard discontinuous Galerkin methods (DG) in order to achieve the non-oscillation property instead of any limiters. Besides, the decomposition algorithm is applied to construct the numerical fluxes, and induced a novel source term approximation to preserve the well-balanced property. In the end, we demonstrate the rigorous one and two-dimensional numerical experiments of the Ripa model, and verify that the well-balanced OFDG schemes have excellent behavior in maintaining the natural high order accuracy within the smooth solution regions, having non-oscillation in the discontinuous solution regions, and successfully capturing the small perturbations near the steady state solutions.
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