The Numerical Simulation With RKDG Method Based On Hyperbolic In Flow And Acoustics Fields

With the leading of high efficiency, high speed and high order accuracy in CFD scope, Computation method focuses on Discontinuous Galerkin Method. The advantages of DG method can be simply summed up as follows: high-precision, high resolving power and high efficient capabilities with discontinuity.This paper uses DG Method to study on four kinds of hyperbolic equation, which contains one-dimensional gas Euler equation, one-dimensional shallow water equation, the acoustic Euler equations in fluid and acoustic stress wave equation in solid. The dispersion of hyperbolic equations with DG method is divided into the following steps: setting an approximate solution function, making integration to disperse equation, setting flux function, constructing limited function, solving Gaussian integral unit; finally, taking on time recurrence to solve time term. In order to compare the calculation accuracy and effectiveness in acoustics field of DG method, this paper introduces the Finite Difference Method (FDM), with which this paper solves the acoustics Euler equation in fluid and acoustics stress wave equation in solid. Based on Leap frog format in FDM, this article puts fluid and solid acoustics equations into three-dimension, while it achieves a good computational result. Finite Difference Method form can be divided into time dispersion and spatial dispersion, for one-order differential equations, time dispersion center differential and space dispersion is often used staggered form. For second-order differential equation, hybrid differential term often uses interlaced format, and the other two items uses two-order accuracy of the three point FDM formats.In order to get better capture of the shock, based on the DG method this paper put forward three shock capture scheme, left upwind, right upwind and double upwind scheme. In different circumstances, the three formats have their own advantages, and the shock wave can be effectively locked in a several grids. In the calculation of intake and exhaust pipe, in order to deal with different boundary conditions, this article uses a unique unilateral interface of DG method to construct flux function, so it effectively solves the discontinuous interface and catches the reflection shock. In shallow water equation the flux function uses TVB feature format, and it effectively tracks the movement shock on the surface of the water. This article put forwards DG method for the calculation of sound field, when it gets well results especially in the fluid sound.In acoustics calculation of fluid field, this article contrasts three-order and four-order accuracy result of the DG method with the Finite Difference Method. From the comparison of results we can get that, with the increasing of accuracy, DG method becomes more excellent than FDM.