黎曼边界条件在高阶精度非结构有限体积方法中的验证与应用

Verification and application of Riemann boundary condition on high-order unstructured finite volume methods

黎曼边界条件是一种弱施加边界条件。通过引入有限波模型,对亚声速入口、出口以及远场边界可采用精确求解黎曼问题来统一处理,有效简化了此类边界条件的施加过程,避免了基于特征关系式与黎曼不变量的推导,并已在二阶精度非结构有限体积方法中取得了较好的数值表现。为进一步验证该边界条件的实用价值,将其推广至高阶精度非结构有限体积离散。通过基于制造解方法(Method of Manufactured Solutions, MMS)的流动、亚声速无黏圆柱绕流及添加初始高斯脉冲扰动的非定常流动这三类数值算例,分别检验了黎曼边界条件在高阶精度非结构有限体积求解器中的数值表现。从计算结果来看,施加黎曼边界条件不会破坏离散格式的设计精度,同时,相比基于一维黎曼不变量的无反射边界条件,黎曼边界条件的施加过程简便,且维持了较好的出口特性,为基于非结构有限体积方法的高精度数值模拟提供了一种更加简单有效的亚声速边界处理方式。

Riemann boundary condition is one of the boundary conditions with weak-imposition approach,which employs the finite wave model to treat boundary conditions of subsonic inlet,outlet and far field by solving the corresponding Riemann problems.Hence,such an imposition process is effectively simplified,and complex derivations based on the characteristic relation and Riemann invariants are completely avoided.By the introduction of this weak-imposition approach,a better numerical performance on second-order unstructured finite volume methods has already been achieved.In order to further verify the application value of this novel boundary condition,it is extended to high-order unstructured finite volume discretization in this study.The numerical performance of this boundary condition is verified in the flow with manufactured solutions(MMS)and real subsonic flows including the inviscid circular flow and the unsteady flow with initial gauss pulse disturbances.Based on computational results,the designed order of accuracy is not deteriorated by the employment of the Riemann boundary condition,and characteristics at the outlet is well reflected compared to the commonly used non-reflective boundary condition based on one-dimensional Riemann invariants.This novel boundary condition is simpler to impose,and provides a more efficient subsonic boundary processing method for high-order numerical simulations based on unstructured finite volume methods.