Abstract. The aim of this work is to provide a promising way to accelerate the structural design procedure and overcome the burden of meshing. The concept of Isogeometric Analysis (IGA) has appeared in recent years and has become a powerful means to eliminate gaps between Computer Aided Design (CAD) and Computer Aided Engineering (CAE), giving a higher fidelity geometric description and better convergence properties of the solution. The Boundary Element Method (BEM) with IGA offers a better, more seamless integration since it uses a boundary representation for the analysis. However, the computational efficiency of IGABEM may be compromised by the dense and unsymmetrical matrix appearing in the calculation, and this motivates the present work. This study introduces an 'a priori' model reduction method in IGABEM analysis aiming to enhance efficiency. The problem is treated as a state evolution process. It proceeds by approximating the problem solution using the most appropriate set of approximation functions, which depend on Karhunen-Loève decomposition. Secondly, the model is re-analysed using a reduced basis, using the Krylov subspaces generated by the governing equation residual for enriching the approximation basis. Finally, the IGABEM calculation combined the model reduction strategy is proposed, which provides accurate and fast re-solution of IGABEM problems compared with the traditional BEM solution. Moreover, the CPU time is drastically reduced. A simple numerical example illustrates the potential of this numerical technique.
This paper proposes a stable and efficient implicit block Lower-Upper Symmetric-Gauss-Seidel (LU-SGS) algorithm-based lattice Boltzmann flux solver (LBFS) for simulation of hypersonic flows. In this method, the finite volume method (FVM) is applied to discretize the Navier-Stokes equations, and the LBFS is utilized to evaluate the numerical flux at the cell interface. In LBFS, the local solution of discrete velocity Boltzmann equation (DVBE) with the non-free parameter D1Q4 lattice Boltzmann model is adopted to reconstruct the inviscid flux across the cell interface, and the viscous flux is approximated by conventional smooth function approach. In order to improve the robustness and convergence rate of the simulation for hypersonic flows, especially for problems with complex geometry, the implicit block LU-SGS algorithm is introduced to solve resultant discrete governing equations. A double cone model at Mach number of Ma = 9.86 is firstly simulated to validate the proposed scheme, and a hypersonic flight vehicle with wings and rudders at Mach number of Ma = 5.56 is then calculated to extend the application in practical engineering problems. Numerical results show that the proposed scheme could offer a more accurate and effective prediction for hypersonic flows.
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