Hydrogeology Journal

, Volume 18, Issue 1, pp 5–23

Three-dimensional benchmark for variable-density flow and transport simulation: matching semi-analytic stability modes for steady unstable convection in an inclined porous box

  • Clifford I. Voss
  • Craig T. Simmons
  • Neville I. Robinson
Paper

Abstract

This benchmark for three-dimensional (3D) numerical simulators of variable-density groundwater flow and solute or energy transport consists of matching simulation results with the semi-analytical solution for the transition from one steady-state convective mode to another in a porous box. Previous experimental and analytical studies of natural convective flow in an inclined porous layer have shown that there are a variety of convective modes possible depending on system parameters, geometry and inclination. In particular, there is a well-defined transition from the helicoidal mode consisting of downslope longitudinal rolls superimposed upon an upslope unicellular roll to a mode consisting of purely an upslope unicellular roll. Three-dimensional benchmarks for variable-density simulators are currently (2009) lacking and comparison of simulation results with this transition locus provides an unambiguous means to test the ability of such simulators to represent steady-state unstable 3D variable-density physics.

Keywords

Analytical solutions Groundwater density/viscosity Numerical modeling Benchmark Variable-density groundwater 

Banc d′essai tri-dimensionnel pour la simulation d′écoulement d′un flux de densité variable: comparaison des modes de convexion uniforme instable dans une boîte poreuse inclinée

Résumé

Ce banc d′essai pour simulation numérique tridimensionnelle (3D) d′un flot d′écoulement souterrain de densité ou d′énergie variable permet de comparer les résultats semi-analytiques de transition d′un mode convectif en régime permanent à un autre, dans une boîte poreuse. Des études expérimentales et analytiques antérieures de flux convectif libre dans un milieu poreux incliné ont montré qu′il existe différents modes de convection possibles dépendant des paramètres du système, géométrie et inclinaison. En particulier, il existe une transition nette entre le mode hélicoïdal, consistant en écoulements longitudinaux descendants surimposés à un flux unicellulaire ascendant et un mode d′écoulement unicellulaire purement ascendant. Des bancs d′essai tri-dimensionnels pour simulations d′écoulements de densité variable manquent actuellement (2009) et la comparaison de simulations avec ce dispositif de transition montre clairement la capacité de tels simulateurs à représenter en 3 dimensions la physique des phénomènes instables en régime permanent.

Estándar de comparación tridimensional para la simulación de flujo de densidad variable y transporte: coincidencia de modo de estabilidad semianalítica para una convección estacionaria inestable en una caja porosa inclinada

Resumen

Este estándar de comparación para simuladores numéricos tridimensionales (3D) de flujo de agua subterránea de densidad variable y transporte de solutos o energía consiste en comparar los resultados de la simulación con la solución semianalítica para la transición de un modo convectivo de estado estacionario a otro de una capa porosa. Experimentos previos y estudios analíticos de flujo convectivo natural en una capa porosa inclinada han demostrado que hay una variedad de posibles modos convectivos dependiendo en los parámetros del sistema, la geometría y la inclinación. En particular, existe una transición bien definida desde el modo helicoidal que consiste en rollos inclinados pendiente abajo superpuestos por sobre un rollo unicelular pendiente arriba a un modo que consiste en un rollo unicelular puro y pendiente arriba. Se carece actualmente (2009) de estándar de comparación tridimensionales para simuladores de densidad variable y la comparación de los resultados de simulaciones con este lugar de transición proporciona un medio inambiguo para testear la habilidad de tales simuladores para representar la física del estado estacionario inestable de densidad variable en 3D.

变密度流和运移模拟的三维基准: 半解析稳定性模式拟合倾斜多孔介质箱中稳态非稳定对流

摘要

这一变密度地下水流和溶质或能量运移的三维数值模拟基准由多孔介质自一个稳态对流模式向另一个稳态对流模式转变的半解析解匹配仿真结果 组成。已有对天然条件下倾斜多孔介质层中对流的实验和解析研究表明, 有很多取决于系统参数、几何形状和倾角的对流模式。特别是由下斜的纵向卷叠加上斜单卷的螺旋式模型到仅仅包括上斜单卷模式的转换, 研究较为清楚。目前 (2009) 缺少变密度流模拟的三维基准, 且模拟结果与这种转换点的比较为检验这种模拟器代表稳态的非稳定3D变密度物理机制的能力提供了确定的方法。

Testes de referência tridimensionais para a simulação de fluxo de densidade variável e de transporte: ajustando modos de estabilidade semi-analíticos para convecção instável e estacionária numa caixa porosa inclinada

Resumo

Este teste de referência (benchmark) para simuladores numéricos tridimensionais (3D) de fluxo de água subterrânea de densidade variável e transporte de soluto ou energia consiste em ajustar os resultados da simulação com a solução semi-analítica para a transição de um modo convectivo estacionário para um outro numa caixa porosa. Os estudos experimentais e analíticos anteriores do fluxo convectivo natural numa camada porosa inclinada mostraram que existe uma variedade de modos convectivos possíveis dependendo dos parâmetros do sistema, da geometria e da inclinação. Em particular, há uma transição bem definida do modo helicoidal consistindo de cilindros longitudinais descendentes sobrepostos a um cilindro unicelular ascendente em relação a um modo consistindo num cilindro unicelular ascendente. Actualmente (2009) há uma falta de testes de referência tridimensionais para simuladores de densidade variável e a comparação dos resultados da simulação com este ponto de transição dá um meio inequívoco para testar a capacidade de tais simuladores representarem a física de densidade variável a 3D, instável e estacionária.

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Clifford I. Voss
    • 1
  • Craig T. Simmons
    • 2
  • Neville I. Robinson
    • 2
  1. 1.US Geological SurveyRestonUSA
  2. 2.Flinders UniversityAdelaideAustralia

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