A comparison of initial conditions for continuous-flow systems

Abstract

An initial condition, which sets the state of a system at a particular time, should describe accurately the physics of the situation and should not create computational artifacts when the governing equations are solved numerically. Drawing on the example of two-phase flow in porous media, we show that unphysical oscillations can mar a solution should the initial condition violate an inflow boundary condition. Tracking these oscillations can increase by orders of magnitude the computer time needed to solve the equations of change. At an internal boundary between two different media, an initial condition that violates the steady-state equations of change produces features that might be equally undesirable. We propose a way to generate initial conditions that avoid these artifacts, viz. by splicing together a solution of the linearized governing equations in the region of change and solutions of the steady-state equations in regions of constancy. We demonstrate our proposal using the situation of two-phase flow in porous media. Our findings are broadly applicable because of the partial analogies among transport of mass, heat and momentum.