Adjoint complement to the volume-of-fluid method for immiscible flows

The paper is concerned with an adjoint complement to the Volume-of-Fluid (VoF) method for immiscible two-phase flows, e.g. air and water, which widely used in marine engineering due its computational efficiency. particular challenge of primal corresponding VoF-approach refers sharp interface treatment featuring discontinuous physical properties. Both continuous system (integration-by-parts) dual compressive convection schemes (summation-by-parts) are derived two prominent schemes, namely High Resolution Interface Capturing Scheme (HRIC) Compressive Arbitrary Meshes (CICSAM). scheme rigorously mirrors Normalized-Variable-Diagram (NVD) stencils. Attention restricted steady state applications. Thus both procedures performed pseudo-time backward integration approach around (pseudo-temporal) converged field. Therefore, experiences same time step size restrictions as system, independent horizon forms a robust well priori stable solution process. analyses equations model problem. An analytical problem initially presented, displays that part does not offer unique, non-trivial solution. As remedy, additional diffusive concentration term introduced equation. imposed heuristic modification violates consistency but strongly regularizes system. can be justified by reference phase-separating diffuse-interface models inheres free mobility-parameter. Numerical results obtained from modified benchmarked against Supplementary, influence on sensitivities simulations two-dimensional flow submerged hydrofoil at Froude Reynolds numbers practical interest discussed range mobility-parameters. final application shape-optimization generic 3D underwater vehicle underlines negligible mobility parameter, even objective functional directly depends manipulated (dual) field quantity.