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In this paper, a higher-order macroscopic model for bi-direction pedestrian flow is presented.For each goup of pedestrian flow, the macroscopic model consists of two-dimensional Euler equations with relaxation.The desired directional motion of each group is to minimize the instantaneous total walking cost from origin to destination, which is described by an Eikonal-type equation.The algorithm to solve the dynamic model is composed of a splitting technique and a finite volume method on an orthogonal grid.Numerical examples of bi-direction pedestrian flow at bottlenecks are designed to validate the rationality of the dynamic model and the effectiveness of the numerical algorithm.