Comparative accuracy and performance assessment of the finite point method in compressible flow problems

• Published in: Computers & fluids Vol. 89; pp. 53 - 65
• Main Authors: Ortega, Enrique, Oñate, Eugenio, Idelsohn, Sergio, Flores, Roberto
• Format: Journal Article Publication
• Language: English
• Published: Elsevier Ltd 20.01.2014; Elsevier
• Subjects: 65 Numerical analysis; Accuracy; Algorithms; Anàlisi numèrica; Assessments; Classificació AMS; Compressible flow; Computational cost; Dinàmica de fluids computacional; Elements finits, Mètode dels; FEM comparison; Finite element method; Finite point method; Matemàtiques i estadística; Mathematical analysis; Mathematical models; Meshfree methods (Numerical analysis); Meshless; Meshless methods; Mètodes en elements finits; Obstacles; Àrees temàtiques de la UPC; Computational cost; Accuracy; Finite point method; Compressible flow; FEM comparison; Meshless
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2013.10.024

•The observed accuracy and performance of the FPM is studied in relation to an equivalent conventional FEM technique.•A 3D transonic inviscid flow problem is employed in the analysis.•Simplifications to improve the computational performance of the FPM are proposed.•The results achieved show that the basic FPM technique is competitive in terms of observed accuracy and computational cost. A comparative assessment of the Finite Point Method (FPM) is presented. Using a wing-fuselage configuration under transonic inviscid flow conditions as reference test case, the performance of the FPM flow solver is compared with an equivalent edge-based Finite Element (FEM) implementation. Efficiency issues have discouraged practical application of meshless methods in the past. Thus, a simplification of the basic FPM technique is proposed in order to reduce the performance gap with respect to classical grid-based algorithms. A comparative evaluation of the accuracy, computational cost and parallel performance of the meshless implementation is carried out with the objective to assess the level of maturity of the technique and identify improvements still required to tackle practical applications. The results obtained show accuracy and performance of the core algorithm comparable to a conventional FEM implementation, thus removing a major obstacle for further developments of the FPM.