New least squares method with geometric conservation law (GC-LSM) for compressible flow computation in meshless method

• Published in: Computers & fluids 2018-08, Vol.172, p.122-146
• Main Authors: Huh, Jin Young, Rhee, Jae Sang, Kim, Kyu Hong, Jung, Suk Young
• Format: Article
• Language: English
• Subjects: AUSMPW; Compressible flow; Conservation; Finite element method; Finite volume method; Fluid dynamics; GC-LSM; Geometric conservation law; Geometry; Hypersonic flow; Lagrange multiplier; Least squares method; Mathematical analysis; Meshless method; Meshless methods; MUSCL limiters; MUSCL schemes; Nozzle flow; Nozzles; Sine waves
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2018.06.010

•A meshless method that overcomes the intrinsic non-conservative feature is proposed.•The geometric conservation law and first-order consistency are satisfied.•This method can accurately and robustly solve compressible flows with a strong shock.•This method does not lose accuracy even in randomly distributed points. In this study, we propose a meshless scheme, GC-LSM (Geometric Conservation Least Squares Method), satisfying the geometric conservation and 1st order consistency. These constraints are introduced in order to overcome the non-conservativeness of the original meshless scheme and imposed by Lagrange multiplier on the least squares method which determines weighting coefficients of the derivative terms. Improvements on the meshless scheme are confirmed through computations with randomly distributed grid points for a sine wave, nozzle flow, and hypersonic flow around blunt body. Combined with AUSMPW + and MUSCL scheme, GC-LSM of the second order accuracy gives non-oscillating solution around a strong shockwave, even for hypersonic flow, and shows its capability comparable to the finite volume method in views of accuracy, robustness, and convergence.