Proposal of Method of Numerically Manufactured Solutions for Code Verification of Elasto-Plastic Problems

Abstract

Many scientific and engineering problems, including soil dynamics problems with elasto-plasticity, are involved in solving partial differential equations numerically. The correctness and accuracy of the solutions have to be checked in a rigorous way, i.e., the code used to solve the problems has to be verified. In the field of fluid dynamics, the method of manufactured solutions (MMS) has been proposed and accepted as a de facto standard for code verification. However, we show in this paper that MMS procedures cannot be used directly for soil dynamics problems considering elasto-plasticity. The main difficulty is due to the soil elasto-plasticity which is generally formulated in a rate form coupled by an algebraic constraint (the yield surface). Instead, we propose the method of numerically manufactured solutions (MNMS) for verifying elasto-plastic problems. The concepts and the workflows of MNMS are explained in detail and two simple demonstrations are presented. Though the numerical demonstrations in the present paper are primitive, the capability of the proposed MNMS, as a general and systematic way for developers and users of numerical simulations to verify their codes being used, should not be underestimated.