An Effective Mesh Deformation Approach for Hull Shape Design by Optimization

A method for the morphing of surface/volume meshes suitable to be used in hydrodynamic shape optimization is proposed. Built in the OpenFOAM environment, it relies on a Laplace equation that propagates the modifications of the surface boundaries, realized by applying a free-form deformation to a subdivision surface description of the geometry, into the computational volume mesh initially built through a combination of BlockMesh with cfMesh. The feasibility and robustness of this mesh morphing technique, used as a computationally efficient pre-processing tool, is demonstrated in the case of the resistance minimization of the DTC hull. All the hull variations generated within a relatively large design space are efficiently and successfully realized, i.e., without mesh inconsistencies and quality issues, only by deforming the initial mesh of the reference geometry. Coupled with a surrogate model approach, a significant reduction in the calm water resistance, in the extent of 10%, has been achieved in a reasonable computational time.

Minimally deformed anisotropic stars by gravitational decoupling in Einstein–Gauss–Bonnet gravity

In this article, we develop a theoretical framework to study compact stars in Einstein gravity with the Gauss–Bonnet (GB) combination of quadratic curvature terms. We mainly analyzed the dependence of the physical properties of these compact stars on the Gauss–Bonnet coupling strength. This work is motivated by the relations that appear in the framework of the minimal geometric deformation approach to gravitational decoupling (MGD-decoupling), we establish an exact anisotropic version of the interior solution in Einstein–Gauss–Bonnet gravity. In fact, we specify a particular form for gravitational potentials in the MGD approach that helps us to determine the decoupling sector completely and ensure regularity in interior space-time. The interior solutions have been (smoothly) joined with the Boulware–Deser exterior solution for 5D space-time. In particular, two different solutions have been reported which comply with the physically acceptable criteria: one is the mimic constraint for the pressure and the other approach is the mimic constraint for density. We present our solution both analytically and graphically in detail.

Ultracompact stars with polynomial complexity by gravitational decoupling

In this work we construct an ultracompact star configuration in the framework of Gravitational Decoupling by the Minimal Geometric Deformation approach. We use the complexity factor as a complementary condition to close the system of differential equations. It is shown that for a polynomial complexity the resulting solution can be matched with two different modified-vacuum geometries.

Gravitationally decoupled non-static anisotropic spherical solutions

This paper is devoted for the formulation of new anisotropic solutions for non-static spherically symmetric self-gravitating systems through gravitational decoupling technique. Initially, we add a gravitational source in the perfect matter distribution for inducing the effects of anisotropy in the considered model. We then decouple the field equations through minimal geometric deformation approach and derive three new anisotropic solutions. Among these, two anisotropic solutions are evaluated by applying specific constraints on anisotropic source and the third solution is obtained by employing the barotropic equation of state. The physical acceptability and stability of the anisotropic models are investigated through energy conditions and causality condition, respectively. We conclude that all the derived anisotropic solutions are physically viable as well as stable.