in this paper a novel numerical approach is presented for solving the transient incompressible fluid flow problems with free surfaces in generalized two-dimensional curvilinear coordinate systems. solution algorithm is a combination of implicit real-time steps and explicit pseudo-time steps. governing fluid flow equations are discretized using a collocated finite-volume mesh. convective terms a...

We present a numerical method for the solution of three-dimensional linear magnetostatic problems by embedding their geometry into symmetric domain and Fourier expansion in symmetry coordinate, leading to set decoupled two-dimensional problems. Special cases include axial translational symmetry. To keep treatment universal, framework decomposition vector potential formulation is developed covar...

Prototypes for automated spatial layout in architecture focus on approaches, which define occupiable space as an orthogonal 2D-grid and use algorithms to allocate each rectangle of the grid to a particular function. However, these approaches are limiting the design to orthogonal spatial layouts. Based on SAT solving techniques, the prototype presented in this paper proposes a methodology for au...

We extend the positivity-preserving method of Zhang & Shu [49] to simulate the advection of neutral particles in phase space using curvilinear coordinates. The ability to utilize these coordinates is important for non-equilibrium transport problems in general relativity and also in science and engineering applications with specific geometries. The method achieves high-order accuracy using Disco...

Difference representations on curvilinear coordinate systems are constructed by first transforming derivatives with respect to cartesian coordinates into expressions involving derivatives with respect to the curvilinear coordinates (the metric coefficients). The derivatives with respect to the curvilinear coordinates are then replaced with difference expressions on the uniform grid in the trans...