FEM approximation of dynamic contact problem for fracture under fluid volume control using generalized HHT-α and semi-smooth Newton methods

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-07-22 DOI:10.1016/j.apnum.2025.07.009

Victor A. Kovtunenko , Yves Renard

引用次数: 0

Abstract

A class of elastodynamic contact problems for fluid-driven cracks stemming from hydro-fracking application is considered in the framework of finite element approximation. The dynamic contact problem aims at finding a non-negative fracture opening and a mean fluid pressure which are controlled by the volume of pumped fracturing fluid. Well-posedness of the fully discrete variational problem is proved rigorously by using the Lagrange multiplier and penalty methods for the minimization problem subjected to both: unilateral and non-local constraints. Numerical solution of the dynamic nonlinear equation is computed in 2D experiments using the semi-smooth Newton and the generalized Hilber–Hughes–Taylor α-method.

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流体体积控制下裂缝动态接触问题的广义HHT-α和半光滑牛顿法有限元逼近

在有限元逼近的框架下，研究了水力压裂过程中流体驱动裂纹的弹动力接触问题。动态接触问题的目的是找到一个非负的裂缝开口和平均流体压力，这是由泵送压裂液的体积控制的。利用拉格朗日乘子和惩罚方法，对单边约束和非局部约束下的最小化问题进行了严格证明，证明了完全离散变分问题的适定性。利用半光滑牛顿法和广义Hilber-Hughes-Taylor α-法在二维实验中计算了动态非线性方程的数值解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.