基于任意Riemann解法器的相容中心型ALE方法
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摘要
深入分析了精确Riemann解法器、MFCAV(Multi Fluid Channel on Averaged Volume)和Dukowicz近似Riemann解法器不能直接应用于相容拉氏方法的原因,通过引入更一般形式的角点算子,成功将以上3种Riemann解法器应用于新相容拉氏方法中;进一步结合高效的网格重分、重映技术,建立了一种基于任意Riemann解法器的相容中心型显式两步任意拉格朗日-欧拉(ALE)方法。将新的ALE方法应用于数值算例中,结果表明,新ALE方法不仅具有新相容拉氏方法的优点,而且具有处理大变形流动问题的能力。
We first deeply analyzed the reason why the exact Riemann sovler,MFCAV(Multi fluid channel on averaged volume)Riemann solver and Dukowicz Riemann solver cannot be applied directly to the compatible Lagrangian method and then,by introducing a new general nodal solver,we successfully applied the 3Riemann solvers to the Lagrangian method.Combing the new Lagrangian method with efficiency remesh and remapping technology,we developed a new cell-centered compatible ALE(Arbitrary Lagrangian and Eulerian)method based on arbitrary Riemann solvers.Several numerical examples show that the new ALE method not only has the advantages of the new compatible Lagrangian method,but also has the ability to deal with the large deformation problems.
We first deeply analyzed the reason why the exact Riemann sovler,MFCAV(Multi fluid channel on averaged volume)Riemann solver and Dukowicz Riemann solver cannot be applied directly to the compatible Lagrangian method and then,by introducing a new general nodal solver,we successfully applied the 3Riemann solvers to the Lagrangian method.Combing the new Lagrangian method with efficiency remesh and remapping technology,we developed a new cell-centered compatible ALE(Arbitrary Lagrangian and Eulerian)method based on arbitrary Riemann solvers.Several numerical examples show that the new ALE method not only has the advantages of the new compatible Lagrangian method,but also has the ability to deal with the large deformation problems.
引文
[1]Loubere R,Shashkov M J.A subcell remapping method on staggered polygonal grids for arbitrary LagrangianEulerian method[J].J Comput Phys,2005,209(1):105-138.
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[3]Addession F L,Carroll D E,Dukowicz J K,et,al.CAVEAT:A computer code for fluid dynamics problem with large distortion and internal slip,LA-10613-MS[R].New Mexico:Los Alamos National Lab,1992.
[4]Tian B L,Shen W D,Liu Y,et al.Numerical comparing of several Godunov type schemes in Lagrangian framework[J].Chinese Journal of Computational Physics,2007,24(5):537-542.(in Chinese)田保林,申卫东,刘妍,等.ALE框架下几种不同Godunov型格式的数值比较[J].计算物理,2007,24(5):537-542.
[5]Maire P H,Abgrall R,Breil J,et al.A cell-centered Lagrangian scheme for two-dimensional compressible flow problems[J].SIAM J Sci Comput,2007,29(4):1781-1824.
[6]Maire P H.A high order cell-centered Lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes[J].J Comput Phys,2009,228(7):2391-2425.
[7]Liu Y,Tian B L,Shen W D,et al.Application of MFCAV Riemann solver to Maires cell-centered Lagrangian method[J].J Comput Math,2015,37(3):286-298.
[8]Li D Y,Xu G R,Shui H S,et al.Two-Dimensional Hydrodynamic Numerical Algorithm[M].Beijing:Science Press,1987.(in Chinese)李德元,徐国荣,水鸿寿,等.二维非定常流体力学数值方法[M].北京:科学出版社,1987.
[9]Winslow A M.Adaptive mesh zoning by the equipotential method,UCID-9062[R].California:Lawrence Livermore National Laboratory,1981.
[10]Benson D J.Momentum advection on a staggered mesh[J].J Comput Phys,1992,100(1):143-162.
[11]Noh W F.Errors for calculations of strong shocks using artifical viscosity and artifical heat flux[J].J Comput Phys,1987,72(1):78-120.
[12]Tian B L,Shen W D,Jiang S,et al.An arbitrary Lagrangian-Eulerian method based on the apaptive Riemann solver for general equations of state[J].Int J Numer Meth Fluids,2009,59(11):1217-1240.
[13]Woodward P,Colella P.The numerical simulation of two-dimensional fluid flow with strong shocks[J].J Comput Phys,1984,54(1):115-173.
[14]Liu Y,Tian B L,Shen W D,et al.The analysis of entropy condition for MFCAV Riemann solver in a compatible Lagrangian method[J].Journal of Computational Mathematics,2015,33(2):1-18.(in Chinese)刘妍,田保林,申卫东,等.MFCAV近似Riemann解法器在相容拉氏方法中的熵条件分析[J].计算数学学报,2015,33(2):1-18.
[15]Brio M,Zakharian A R,Webb G M.Two-dimensional Riemann solver for Euler equations of gas dynamics[J].J Comput Phys,2001,167(1):177-195.
[2]Duckowicz J K,Meltz B J A.Vorticity errors in multidimensional Lagrangian codes[J].J Comput Phys,1992,99(1):115-134.
[3]Addession F L,Carroll D E,Dukowicz J K,et,al.CAVEAT:A computer code for fluid dynamics problem with large distortion and internal slip,LA-10613-MS[R].New Mexico:Los Alamos National Lab,1992.
[4]Tian B L,Shen W D,Liu Y,et al.Numerical comparing of several Godunov type schemes in Lagrangian framework[J].Chinese Journal of Computational Physics,2007,24(5):537-542.(in Chinese)田保林,申卫东,刘妍,等.ALE框架下几种不同Godunov型格式的数值比较[J].计算物理,2007,24(5):537-542.
[5]Maire P H,Abgrall R,Breil J,et al.A cell-centered Lagrangian scheme for two-dimensional compressible flow problems[J].SIAM J Sci Comput,2007,29(4):1781-1824.
[6]Maire P H.A high order cell-centered Lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes[J].J Comput Phys,2009,228(7):2391-2425.
[7]Liu Y,Tian B L,Shen W D,et al.Application of MFCAV Riemann solver to Maires cell-centered Lagrangian method[J].J Comput Math,2015,37(3):286-298.
[8]Li D Y,Xu G R,Shui H S,et al.Two-Dimensional Hydrodynamic Numerical Algorithm[M].Beijing:Science Press,1987.(in Chinese)李德元,徐国荣,水鸿寿,等.二维非定常流体力学数值方法[M].北京:科学出版社,1987.
[9]Winslow A M.Adaptive mesh zoning by the equipotential method,UCID-9062[R].California:Lawrence Livermore National Laboratory,1981.
[10]Benson D J.Momentum advection on a staggered mesh[J].J Comput Phys,1992,100(1):143-162.
[11]Noh W F.Errors for calculations of strong shocks using artifical viscosity and artifical heat flux[J].J Comput Phys,1987,72(1):78-120.
[12]Tian B L,Shen W D,Jiang S,et al.An arbitrary Lagrangian-Eulerian method based on the apaptive Riemann solver for general equations of state[J].Int J Numer Meth Fluids,2009,59(11):1217-1240.
[13]Woodward P,Colella P.The numerical simulation of two-dimensional fluid flow with strong shocks[J].J Comput Phys,1984,54(1):115-173.
[14]Liu Y,Tian B L,Shen W D,et al.The analysis of entropy condition for MFCAV Riemann solver in a compatible Lagrangian method[J].Journal of Computational Mathematics,2015,33(2):1-18.(in Chinese)刘妍,田保林,申卫东,等.MFCAV近似Riemann解法器在相容拉氏方法中的熵条件分析[J].计算数学学报,2015,33(2):1-18.
[15]Brio M,Zakharian A R,Webb G M.Two-dimensional Riemann solver for Euler equations of gas dynamics[J].J Comput Phys,2001,167(1):177-195.