How to select the best sites for exploiting lithium from hydro-thermal sources, or how to ensure long-term storage of CO2 in deep aquifers, are major challenges requiring a deep understanding of fluid movements in the subsurface. To meet these energy transition challenges, high-fidelity numerical simulation is an indispensable tool requiring efficient usage of high-performance computing resources. The most memory and time-consuming part of such simulation consist in solving non-symmetric, sparse, ill-conditioned systems can even contribute to 80\% of the simulation time. They are in general solved by using iterative Krylov subspace solvers. To efficiently use homogeneous and heterogeneous computing resources, exploiting different levels of parallelism should be studied. The demand for a fast solution of simulations coupled with new computing architectures drives the need for an appropriate programming model, challenging algorithms, low level [3], software architecture, etc.. This paper focuses on both x86 64 and ARM (Ampere Altra and Fujitsu A64fx) hardware architectures with a particular focus on different SIMD instructions. We study the relevant key points to address for reaching more compute-intensive at the node level and parallel scalability up to 20,000 computing cores. We overcome the hardware related issues by relying on a strategy based on object-oriented facilities, in order to be able to address in an extensible way the different programming models for both application platforms [2] and the plugged linear solver library. The proposed software architecture allows to design a linear solver library composing the appropriate building blocks to construct the preconditioned linear solver for a given target hardware architecture. The scalability of the proposed solution is evaluated both in the CO2 storage application and in the ShArc demonstrator(github.com/arcaneframework/sharc) for solving multi-phase flow transport in porous media. For the considered applications, a comparison in terms of performance and number of iterations with other linear solver libraries as Trilinos [1] is also carried out.