# Advanced Mathematical Modeling in Engineering

**Type:** Topics  
**Canonical URL:** https://scholariq.org/topics/advanced-mathematical-modeling-in-engineering/

## Facts

| Field | Value |
| --- | --- |
| Description | This cluster of papers focuses on the development and application of multiscale methods for analyzing heterogeneous systems, particularly in the context of homogenization, finite element simulations, and porous media flow. The papers cover topics such as upscaling techniques, subsurface flow simulation, coarse-grained computation, and the use of microscopic simulators to perform system-level analysis. |
| Domain | Physical Sciences |
| Field | Computer Science |
| OpenAlex ID | t12100 |
| Works | 17 |

## Topic papers all

Showing 15 of 17.

- [One- and Two-Equation Models for Transient Diffusion Processes in Two-Phase Systems](https://scholariq.org/papers/one-and-two-equation-models-for-transient-diffusion-processes-in-two-phase/)
- [Two-medium treatment of heat transfer in porous media: numerical results for effective properties](https://scholariq.org/papers/two-medium-treatment-of-heat-transfer-in-porous-media-numerical-results-for/)
- [On the Stability and Accuracy of Least Squares Approximations](https://scholariq.org/papers/on-the-stability-and-accuracy-of-least-squares-approximations/)
- [Transport in ordered and disordered porous media: volume-averaged equations, closure problems, and comparison with experiment](https://scholariq.org/papers/transport-in-ordered-and-disordered-porous-media-volume-averaged-equations/)
- [Transport in ordered and disordered porous media I: The cellular average and the use of weighting functions](https://scholariq.org/papers/transport-in-ordered-and-disordered-porous-media-i-the-cellular-average-and-the/)
- [Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?](https://scholariq.org/papers/homogenization-via-formal-multiscale-asymptotics-and-volume-averaging-how-do-the/)
- [Doping effects on coarsening of Y<sub>2</sub>BaCuO<sub>5</sub> phase in liquid](https://scholariq.org/papers/doping-effects-on-coarsening-of-y-sub-2-sub-bacuo-sub-5-sub-phase-in-liquid/)
- [A Comparison of Various Methods for the Numerical Evaluation of Porous Media Permeability Tensors from Pore-Scale Geometry](https://scholariq.org/papers/a-comparison-of-various-methods-for-the-numerical-evaluation-of-porous-media/)
- [Modelling of large multilayered aquifer systems: Theory and applications](https://scholariq.org/papers/modelling-of-large-multilayered-aquifer-systems-theory-and-applications/)
- [On the Application of the Continuous Galerkin Finite Element Method for Conservation Problems](https://scholariq.org/papers/on-the-application-of-the-continuous-galerkin-finite-element-method-for/)
- [Modeling non-equilibrium mass transport in biologically reactive porous media](https://scholariq.org/papers/modeling-non-equilibrium-mass-transport-in-biologically-reactive-porous-media/)
- [Approximate solution of the Bagley–Torvik equation by hybridizable discontinuous Galerkin methods](https://scholariq.org/papers/approximate-solution-of-the-bagley-torvik-equation-by-hybridizable-discontinuous/)
- [Quasilinear abstract parabolic evolution equations and exponential attractors](https://scholariq.org/papers/quasilinear-abstract-parabolic-evolution-equations-and-exponential-attractors/)
- [Stabilising terminal cost and terminal controller for ℓ&lt;inf&gt;asso&lt;/inf&gt;-MPC: enhanced optimality and region of attraction](https://scholariq.org/papers/stabilising-terminal-cost-and-terminal-controller-for-l-and-lt-inf-and-gt-asso/)
- [Dynamic topology optimization of 3D-Printed transtibial orthopedic implant using tunable isotropic porous metamaterials](https://scholariq.org/papers/dynamic-topology-optimization-of-3d-printed-transtibial-orthopedic-implant-using/)

## Topic primary papers

- [Two-medium treatment of heat transfer in porous media: numerical results for effective properties](https://scholariq.org/papers/two-medium-treatment-of-heat-transfer-in-porous-media-numerical-results-for/)
- [Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?](https://scholariq.org/papers/homogenization-via-formal-multiscale-asymptotics-and-volume-averaging-how-do-the/)
- [Modeling non-equilibrium mass transport in biologically reactive porous media](https://scholariq.org/papers/modeling-non-equilibrium-mass-transport-in-biologically-reactive-porous-media/)

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Source: ScholarIQ — public research metadata, principally OpenAlex. See https://scholariq.org/sources/ for provenance and https://scholariq.org/methodology/ for what these figures mean.