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Numerical Results

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A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs

Part of the book series: Lecture Notes in Geosystems Mathematics and Computing ((LNGMC))

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Abstract

As we developed a method of fundamental solutions in quasistatic poroelasticity in the previous chapter, this chapter is dedicated to the application of said method. First, we give some details on the implementation of the method for solving initial boundary value problems of quasistatic poroelasticity on the square (−1, 1)2. This introduces several method parameters which can be organized in three groups. Using several examples with different types of boundary conditions and different behavior, each group is investigated separately with regard to its influence on the performance of the method of fundamental solutions which is judged by approximation quality. Concentrating on well performing parameter method, we investigate the distribution of approximation errors in time and space. Next, we compare results using a sophisticated vs. a simple solution scheme for the resulting system of linear equations. This is followed by a comparison of results produced by the different methods of fundamental solutions developed in the previous chapter. Moreover, we briefly investigate whether a recently suggested variant of the method of fundamental solutions for time-dependent problems is applicable in quasistatic poroelasticity. The chapter is rounded out by a short discussion on the approximation of solutions with steeper gradients and an exemplary application of the method of fundamental solutions for an initial boundary value problem on the cube (−1, 1)3.

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Notes

  1. 1.

    It is usually not necessary to define the corresponding pseudo-boundary \(\hat{\varGamma }\) explicitly.

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  1. AG Geomathematik, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Matthias Albert Augustin

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  1. Matthias Albert Augustin
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Augustin, M.A. (2015). Numerical Results. In: A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs. Lecture Notes in Geosystems Mathematics and Computing. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-17079-4_6

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