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...

Quantum mechanics and general relativity are completely compatible when space-time coordinate systems are eliminated from physics. Standard practice attempts to remove coordinate influence through invariance because it is recognized that coordinates are physically meaningless. But this is shown to be insufficient. This paper investigates a trans-coordinate physics in which space-time coordinate...

In this article, the improved space-time conservation element and solution element (CESE) method are used to simulate the dynamic treatment of the hydrocracking reactor. The dynamic model consists of four lumps: vacuum gas oil (VGO), middle distillate, naphtha, and gas which is dissolved by this method. The offered method can solve the partial differential equations caused by the reactions insi...

Robustness of computations in engineering is one of key issues as it is necessary to solve technical problems leading to ill conditioned solutions. Therefore the robustness and numerical stability is becoming a key issue more important that the computational time. In this paper we will show selected computational issues in numerical precision, well known cases of failures in computations. The E...