多物理程序正确性验证与可信度确认方法研究

In the field of the large science and engineering on national defense, many phenomena and accidents are complicated in process of multi-physics coupling. These technology and methods has become an obstacle to block the research in science theory, the precision design in engineering and the performance assessment on system, which are the technology of correctness verification and the methods of the confidence validation in modeling and simulation. These seriously restrict the ability of the independent creativity and innovation in the frontier area of application. A series of ambitious plans, such as ASC, have been carried out in USA. Its aim is to develop some applied software in order to improve the predict ability and feasibility. This project will consider the physics models, calculation methods and code design altogether in the process of developing the multi-physics codes. The refine principles of function points and checking points of the multi-physics codes are studied. The basic framework, the implementation flow chart and criterion are set up in the verification and validation for Modeling and simulation of the multi-physics codes. The technology of correctness verification is studied by the method of manufactured solution and the grid convergence index in Lagrange codes. The method of the confidence validation is researched through the sensitivity analysis of many parameters, the cumulative distribution function of error and the polynomial chaos method of the uncertainty quantification in the Modeling and simulation. The method of the confidence assessment of the validation domain and prediction domain is explored. The corresponding analysis software is developed and the benchmark library for the correctness verification and the confidence validation in the multi-physics code is built. Finally, the project will apply above methods on a present hydrodynamics code to certify its effectiveness and feasibility.

在国防重大科学与工程高端应用领域，许多现象与事件都是多物理耦合的复杂过程。多物理程序建模与模拟的正确性验证技术与可信度确认方法已成为阻碍科学理论探索、工程精密化设计和系统性能评估的绊脚石，严重制约着高端应用领域自主创新的能力。美国推出ASC 等一系列宏伟计划，其目的就是要发展强预测能力的高可信度应用软件。本项目提出将多物理程序研发涉及的物理建模、计算方法与程序研制一体化考虑，研究多物理程序检查点及功能点细化原则，构建多物理程序建模与模拟验证与确认的基本框架和流程，研究拉氏程序人为解构造方法、网格收敛指标的正确性验证技术；研究建模与模拟中众多参数敏感度分析、误差累积分布函数表征、不确定度多项式混沌量化的可信度确认方法；探索确认域与预测域建模与模拟可信度评估方法，研制相关的分析软件包，建立多物理程序正确性验证与可信度确认的基准库。并将方法用于多物理程序，以检验它的可行性和有效性。

在国家重大工程和产品设计等量大领域，许多现象都是多物理耦合的问题，描述其过程的数学模型往往是高度非线性的偏微分方程组。此模型涉及流体力学方程（质量、动量、能量）和状态方程、本构关系等辅助方程，很难得到解析解，在计算机上进行数值求解已成为重要的手段。数值求解可以真实、全过程、全时空、反复精密地进行。但数值模拟软件的正确性与模拟结果的可信度严重阻碍着软件的推广使用和“自造血能力”，制约着自主创新的能力。验证、确认和不确定度量化（V&V&UQ）是发展高可信度数值仿真软件的重要方法，甚至是唯一途径。.本项目将“物理建模、数值建模、软件研制、数值实验、预测评估”五位一体考虑，发展了多物理程序V&V&UQ的相关术语、概念、基本原理、基本活动、实施流程等，构建了多物理程序建模与模拟V&V&UQ的框架，可有效指导多物理程序的V&V&UQ。结合多物理软件验证的全生命周期，提出了三阶段十五节点的软件质量保证程序验证技术，可有效控制多物理程序的软件质量保证验证实施。采用HTML标准格式，构建了流体力学程序测试模型基本库，发展了三阶段软件测试的验证技术，能为多物理程序产生各种模型测试实例，有效测试程序。结合拉氏有限体积格式，提出了格式精度、对称性、守恒性的数学基本理论验证技术。基于方程右端加源项的思想，构造了平面、柱坐标系下拉氏方程的人为构造解，发展了网格收敛指标及算法实施正确性的验证技术。基于爆轰流体力学程序的功能，提出了功能验证技术。基于炸药爆轰过程，提出了多物理程序模型分层确认方法，构建了爆轰流体力学多物理程序实施确认的层级，发展了多因素敏感度分析、代理模型、高斯过程和残差最小、贝叶斯的不确定性量化方法，提出了基于误差马尾图量化置信度、概率盒的评估方法，有效实施了模型确认。该项目基本形成的中国流体力学多物理程序V&V&UQ的理论体系，该体系具有广泛的辐射性和示范性，可以快速应用到其它领域。该项目多次获奖，得到国内专家的认可。