MLP高阶重构格式应用

Application on MLP high order reconstruction scheme

在有限体积框架下,利用MLP(multi-dimensional limiting process)系列重构格式结合HLLHLLC(Harten-Lax-van Leer with contact)近似黎曼求解器,同时引入激波探测函数进一步降低MLP在光滑流动区域的数值耗散,数值模拟了超声速前台阶流动、结冰翼型的非定常流动、高超声速双楔流动和DLR F6-WB跨声速流场,研究了MLP系列格式在可压缩复杂流场中的表现.结果表明:在多维空间中,MLP格式能够在如强斜激波与网格线不重合等复杂流场数值模拟中保持严格的流场单调性;具有和传统MUSCL(monotone upstream-centered schemes for conservation laws)格式类似的计算效率,可以实现5阶,甚至更高阶重构;数值耗散更低,捕获更准确的激波位置,对航空工程数值模拟具有重要意义.

Under the frame of finite volume methodology, MLP （multi-dimensional lim- iting process） scheme was further modified by introducing a shock-detect function to decrease the numerical dissipation in smooth regions, then supersonic flow over facing step, unsteady flow over an airfoil with ice accretion, hypersonic flow over double wedge configuration flow and subsonic flow over DLR F6-WB complex configuration were investigated by utilizing MLP high order reconstruction scheme and HLL-HLLC （Harten-Lax-van Leer with contact） approximate Riemann solver to validate the performances of proposed schemes in sophisticat- ed compressible flow simulations. The research illustrates that. MLP can keep strict mono- tone flow characteristics even in the complex high-dimension fluid simulations consisting of strong oblique shock waves not aligned with grids; it has the similar computational efficiency compared with traditional MUSCL （monotone upstream-centered schemes for conservation laws） scheme and can achieve fifth or even higher order reconstruction; it features low nu- merical dissipation so that more accurate shock position can be captured, therefore MLP scheme is promising for aerospace engineering applications.