Matthew Wilkinson, Javier Villarreal, Andrew Meade^*

CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.3, pp. 1373-1393, 2021, DOI:10.32604/cmes.2021.017883 - 25 November 2021

Abstract A meshless and matrix-free fluid dynamics solver (SOMA) is introduced that avoids the need for user generated and/or analyzed grids, volumes, and meshes. Incremental building of the approximation avoids creation and inversion of possibly dense block diagonal matrices and significantly reduces user interaction. Validation results are presented from the application of SOMA to subsonic, compressible, and turbulent flow over an adiabatic flat plate. More >

Arash Mehraban¹, Henry Tufo¹, Stein Sture², Richard Regueiro^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.3, pp. 1283-1303, 2021, DOI:10.32604/cmes.2021.017476 - 25 November 2021

Abstract Higher-order displacement-based finite element methods are useful for simulating bending problems and potentially addressing mesh-locking associated with nearly-incompressible elasticity, yet are computationally expensive. To address the computational expense, the paper presents a matrix-free, displacement-based, higher-order, hexahedral finite element implementation of compressible and nearly-compressible (ν → 0.5) linear isotropic elasticity at small strain with p-multigrid preconditioning. The cost, solve time, and scalability of the implementation with respect to strain energy error are investigated for polynomial order p = 1, 2, 3, 4 for compressible elasticity, and p = 2, 3, 4 for nearly-incompressible elasticity, on different number More >