An adaptive WENO algorithm for one-dimensional convection-dominated partial differential equations

In this work, a versatile numerical algorithm was proposed for solving one-dimensional nonlinear convection-dominated partial differential equations as these found in the simulation of diverse chemical engineering applications. The proposed algorithm uses a fully adaptive scheme, in which both the grid spacing and the time discretization are dynamically adjusted. It uses a finite volume discretization with a variable number of grid cells and an explicit time integration with time-step control. The high-order Weighted Essentially Non-Oscillatory (WENO) scheme on non-uniform grid was combined with a grid refinement technique based on the equitable distribution principle and a spatial regularization procedure. The time-stepping procedure as well as some implementation issues are minutely discussed. The capability and efficiency of the new algorithm was demonstrated through the numerical simulation of five chemical engineering applications: the Viscous Burgers Equation, a Chromatographic column, the Buckley-Leverett Equation, and two examples of reaction-convection systems. For all analyzed cases, it was verified that the number of grid cells required to capture steep gradients can be greatly reduced with the proposed grid adaptation scheme. (C) 2019 Elsevier Ltd. All rights reserved.