A high-resolution mapped grid algorithm for compressible multiphase flow problems

Nonlinear preconditioning for efficient and accurate interface capturing in simulation of multicomponent compressible flows

“…(11). The preconditioned density correction equation (15) along with the level set reinitialization equation (10) constitutes a preconditioned interface sharpening technique for countering the artificial smearing of the material interface.…”

“…The primary reasons for our choice of high-order constrained reinitialization method are its simplicity and its effectiveness in anchoring the ψ = 0 isocontour [110]. The next step of the interface sharpening technique concerns discretization of the transformed density correction equation (15). This can be accomplished through standard second-order accurate central differences for the first and second derivatives.…”

“…This tradeoff between the accuracy with which the density correction equation and the flow solver can be discretized necessitates a careful selection of the interface width through h and a control of the discretization errors in the approximation of Eq. (15).…”

“…(15) in multiple dimensions. The familiar 9 point and 27 point isotropic differences for approximation of Laplacian in two and three dimensions, respectively, are routinely employed in phase field simulations in order to minimize grid anisotropy effects (e.g.…”

“…The use of oscillation-free single fluid discretization schemes for numerical simulation of multiphase compressible flows is an effective and well established strategy [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. These schemes use enforcement of appropriate constraints across the diffuse material interface (such as preservation of pressure and normal velocity continuity (cf.…”