Some aspects and current needs for geothermal reservoir modeling. First results obtained with ComPASS platform.
Geothermal energy is a carbon-free steady subsurface energy source with low environmental impact.
Numerical modeling has become essential in all phases of geothermal operations. It is used in the exploration phases to assess the geothermal potential, validate conceptual hypothesis and help well siting. Considering the current geothermal modeling state of the art there is an established need for a better integration of static and dynamic models opening the door for a new generation of conceptual geothermal reservoir models.
We will present preliminary results obtained with the ComPASS platform (Computing Parallel Architecture to Speed up Simulation), which is a parallel code (MPI) that we are currently developing to tackle such problems. It can simulate compositional multiphase Darcy flow in heterogeneous porous media, taking into account the coupling of the mass balance of each component, the energy conservation, the pore volume conservation and the thermodynamical equilibrium as well as phase change. On important point is the possibility to take into account 2D Darcy flow in a discrete fracture network including the mass and energy exchanges between the surrounding matrix and the fractures through an asymptotic model leading to the so called hybrid dimensional Darcy flow model. The computational efficiency of the model is assessed on a few geothermal test cases ranging from the simulation of a tracer in a faulted reservoir to the simulation of a thermal gas liquid Darcy flow the Boiling high energy geothermal reservoir.
High order implicit/explicit transport Discontinuous Galerkin solvers
and applications to CFL-less fluid solvers.
We present an implicit Discontinuous Galerkin solver for the transport
equation. Because of the upwind nature of the numerical flux the linear
system in the implicit step is block triangular. The scheme does not
require costly linear system inversion and is well adapted to a
task-based parallel implementation. It also leads to very efficient
fluid solvers without CFL condition. The main difficulty however is to
increase the precision of the time integrator.
Tuesday, July 26, 9:00 AM
Pascal Hénon (Total)
Linear Solvers for Reservoir simulation
In this presentation, we will first present the main goals and principles of reservoir simulation. Then we will focus on linear systems that arise in such simulation. The main HPC challenge is to solve those systems efficiently on massively parallel computers. The specificity of those systems is that their convergence is mostly governed by the elliptic part of the equations and the linear solver needs to take advantage of it to be efficient. The reference method in reservoir simulation is CPR-AMG which usually relies on AMG to solve the quasi elliptic part of the system. We will present some works on improving AMG scalability for the reservoir linear systems (work done in collaboration with CERFACS). We will then introduce an on-going work with INRIA to take advantage of their enlarged Krylov method (EGMRES) in the CPR method.
High Performance Computing with Feel++ : Applications and Numerical methods
I will review (some of) the HPC solution strategies developed in Feel++. We present our advances in developing a language specific to partial differential equations embedded in C++. We have been developing the Feel++ framework (Finite Element method Embedded Language in C++) to the point where it allows to use a very wide range of Galerkin methods and advanced numerical methods such as domain decomposition methods including mortar and three fields methods, fictitious domain methods or certified reduced basis. We shall present an overview of the various ingredients as well as some illustrations. The ingredients include a very expressive embedded language, seamless interpolation, mesh adaption, seamless parallelisation. As to the illustrations, they exercise the versatility of the framework either by allowing the development and/or numerical verification of (new) mathematical methods or the development of large multi-physics applications--- e.g. fluid-structure interaction using either
an Arbitrary Lagrangian Eulerian formulation or a levelset based one; high field magnets modeling which involves electro-thermal, magnetostatics, mechanical and thermo-hydraulics model; ... --- The range of users span from mechanical engineers in industry, physicists in complex fluids, computer scientists in biomedical applications to applied mathematicians thanks to the shared common mathematical embedded language hiding linear algebra and computer science complexities.
Philippe Ricoux (Total SA / Direction Scientifique)
Multiple applications of High Performance Computing and Numerical Simulations in TOTAL Group
Facing energy future is one of the large challenges of the world, with numerous implications for R&D strategy of energy companies.
One of the TOTAL R&D missions is the development of competences on advanced technologies, such as Advanced Computing (HPC), Material sciences, Biotechnologies, Nanotechnologies, New analytical techniques, IT Technologies.
HPC allows also tackling the challenge in code coupling: both a horizontal direction -multi-physics-, (chemistry and transport, or structural mechanics, acoustics, fluid dynamics, and thermal heat transfer, ...) and in the vertical direction -multi-scale models- (i.e. from continuum to mesoscale to molecular dynamics to quantum chemistry) which requires bridging space and time scales that span many orders of magnitude.
This leads to improve at the same time more accurate physical model and numerical methods and algorithms and these improvements of numerical simulations will be illustrated by their application, use and impact in TOTAL strategic activities such as:
seismic, depth imaging by solving waves equation; oil reservoir modeling by solving transport, thermal and chemical equations; multi scale process modeling and control, such as slurry loop process; mechanical structures and geomecanics.
Efficient iterative solvers: FETI methods with multiple search directions
In domain decomposition methods, most of the computational cost lies in
the successive solutions of the local problems in subdomains via
forward-backward substitutions and in the orthogonalization of interface
search directions. All these operations are performed, in the best case,
via BLAS-1 or BLAS-2 routines which are inefficient on multicore systems
with hierarchical memory.
A way to improve the parallel efficiency of the method consists in
working with several search directions, since multiple forward-backward
substitutions and reorthogonalizations involve BLAS-3 routines.
In the case of a problem with several right-hand-sides, using a block
Krylov method is a straightforward way to work with multiple search
directions. This will be illustrated with an application in
electromagnetism using FETI-2LM method.
For problems with a single right-hand-side, deriving several search
directions that make sense from the optimal one constructed by the
Krylov method is not so easy. The recently developed S-FETI method
gives a very good approach that does not only improve parallel
efficiency but can also reduce the global computational cost in the
case of very heterogeneous problems.
HPC Challenges: Democratization and Exascale stakes
Thursday, July 28, 2:00 PM
Martin Vohralik (INRIA Paris)
A posteriori error estimates and solver adaptivity in numerical simulations
We review how to bound the error between the unknown weak solution of
a PDE and its numerical approximation via a fully computable a
posteriori estimate. We focus on approximations obtained at an
arbitrary step of a linearization (Newton-Raphson, fixed point, ...)
and algebraic solver (conjugate gradients, multigrid, domain
decomposition, ...). Identifying the discretization, linearization,
and algebraic error components, we design local stopping criteria
which keep them in balance. This gives rise to a fully adaptive
inexact Newton method. Numerical experiments are presented in
confirmation of the theory.
Optimized Schwarz waveform relaxation methods : theory and applications
We review Optimized Schwarz waveform relaxation methods which are
space-time domain decomposition methods. The main ideas are explained
on the heat equation, and extension to advection-diffusion equations
are illustrated by numerical results. We present the Schwarz for
TrioCFD project, which aims at using this kind of methods for the
Stokes equations.
Parametrized Model Order Reduction for Component-to-System Synthesis
Parametrized PDE (Partial Differential Equation) Apps are PDE solvers
which satisfy stringent per-query performance requirements: less-than
or approximate 5-second problem specification time; less-than or
approximate 5-second problem solution time, field and outputs;
less-than or approximate 5% solution error, specified metrics;
less-than or approximate 5-second solution visualization
time. Parametrized PDE apps are relevant in many-query, real-time, and
interactive contexts such as design, parameter estimation, monitoring,
and education.
In this talk we describe and demonstrate a PDE App computational
methodology. The numerical approach comprises three ingredients:
component => system synthesis, formulated as a static-condensation
procedure; model order reduction, informed by evanescence arguments at
component interfaces (port reduction) and low-dimensional parametric
manifolds in component interiors (reduced basis techniques); and
parallel computation, implemented in a cloud environment. We provide
examples in acoustics and also linear elasticity.
The semi-Lagrangian method using oblic interpolation
We develop a semi-Lagrangian scheme adapted to the case where the solution presents low oscillations in some fixed direction. The method is analyzed for the 2D constant advection and applied to the numerical resolution of the gyrokinetic equations.
Data-driven wildfire behavior modelling: Focus on front level-set data assimilation
A front data assimilation system named FIREFLY has been developed at CERFACS in collaboration with the University of Maryland to better estimate the environmental conditions (biomass properties, near-surface wind). We discuss the sequential application of the ensemble Kalman filter (EnKF) in FIREFLY for correcting in a spatially-distributed way, input parameters in order to better track the fire front position. In particular, using a polynomial chaos surrogate to mimic the wildfire spread model in the EnKF algorithm was found in collaboration with LIMSI to be a promising strategy to reduce the computational cost of FIREFLY.
We also discuss the way we represent the distance between simulated and observed fronts. In the CEMRACS project, a new discrepancy operator will be introduced to better represent the match (or mismatch) between simulated fronts and mid-infrared observations in collaboration with INRIA. This front level-set data assimilation derived from image processing and designed for electrophysiology will be extended to wildfire spread monitoring.
In this presentation, we give an overview of the TrioCFD project
(previously named "Trio_U"). TrioCFD is a programmable software for
Computational Fluid Dynamics (CFD), based on the TRUST platform
(TRio_U Software for Thermohydraulics). This project is supported by
the Nuclear Energy Department of the French Atomic Agency (CEA).
The physical models developed, the numerical methods used and the
massive parallelism of the TrioCFD code allow to simulate various
problems, going from local simulations of two-phase flows to
simulations of turbulent flows on industrial facilities such as
portions of nuclear reactors. Some typical examples of recent
qualification studies in topics mainly related to nuclear domain are
presented here. Most of them correspond to international experimental
or industrial facilities and combine various complex physical
phenomena.
Thursday, August 4, 9:00 AM
Vincent Perrier (Inria)
Direct numerical simulation of aeronautical flows with the library Aerosol
In this talk, we will give details on the derivation and implementation of a scheme for computing compressible flows with the discontinuous Galerkin method. The Aerosol library will be presented, and some results will be given for the parallelization and on some aeronautical tests. Last, we will present the current developments within the library, especially within the hodin project in this Cemracs.
Friday, August 5, 9:00 AM
Sophie Valcke (CERFACS)
Code coupling for climate modelling
Coupling numerical models, i.e. implementing synchronised exchanges of information between
these models, is a central issue in many research fields such
as climate modelling, data assimilation, or computational
fluid dynamics. In climate modelling, different approaches
exist to couple the components of Earth System Models (ESMs).
In this talk, we will first review the different technical
solutions that exist to implement the coupling between
different codes. We will then briefly describe few existing
coupling technologies that are used in different climate
modelling groups in Europe and in the US, such as the OASIS
coupler developed at Cerfacs and the Earth System Modelling
Framework used in the US.
Modeling and data assimilation in cardiac electrophysiology
In this talk we overview some of the challenges of cardiac modeling and simulation of the electrical depolarization of the heart. In particular, we will present a strategy allowing to avoid the 3D simulation of the thin atria depolarization but only solve an asymptotic consistent model on the mid-surface. In a second part, we present a strategy for estimating a cardiac electrophysiology model from front data measurements using sequential parallel data assimilation strategy.
High performance climate modelling : mimetic finite differences, and beyond ?
Climate models simulate atmospheric flows interacting with many physical processes. Because they address long time scales, from centuries to millennia, they need to be efficient, but not at the expense of certain desirable properties, especially conservation of total mass and energy. Most of my talk will explain the design principles behind DYNAMICO, a highly scalable unstructured-mesh energy-conserving finite volume/mimetic finite difference atmospheric flow solver and potential successor of LMD-Z, a structured-mesh (longitude-latitude) solver currently operational as part of IPSL-CM, the Earth System Model developed by Institut Pierre Simon Laplace (IPSL). Specifically, the design exploits the variational structure of the equations of motion and their Hamiltonian formulation, so that the conservation of energy requires only that the discrete grad and div operators be compatible, i.e. that a discrete integration by parts formula holds.
I will finish my talk by sketching how the desirable properties of DYNAMICO may be obtained with a different approach based on mixed finite elements (FEM). Indeed while DYNAMICO is very fast and scalable, it is low-order and higher-order accuracy may be desirable. While FEM methods can provide higher-order accuracy, they are computationally more expensive. They offer a viable path only if the performance gap compared to finite differences is not too large. The aim of the CEMRACS project A-HA is to evaluate how wide this gap may be, and whether it can be narrowed by using a recently proposed duality-based approach to assemble the various matrices involved in a FEM method.
Direct and inverse biomechanical modeling of the heart
The heart undergoes some highly complex multi-scale multi-physics phenomena that must be accounted for in order to adequately model the biomechanical behavior of the complete organ. In this respect, a major focus of our work has been on formulating modeling ingredients that satisfy the most crucial thermomechanical requirements - in particular as regards energy balances - throughout the various forms of physical and scale-related couplings. This has led to a "beating heart" model for which some experimental and clinical validations have already been obtained. Concurrently, with the objective of building "patient-specific" heart models, we have investigated some original approaches inspired from data assimilation concepts to benefit from the available clinical data, with a particular concern for medical imaging. By combining the two fundamental sources of information represented by the model and the data, we are able to extract some most valuable quantitative knowledge on a given heart, e.g. as regards some uncertain constitutive parameter values characterizing a possible pathology, with important perspectives in diagnosis assistance. In addition, once the overall uncertainty has been adequately controlled via this adjustment process, the model can be expected to become "predictive", hence should provide clinically-relevant quantitative information, both in the current state of the patient and under various scenarii of future evolutions, such as for therapy planning.
Godunov type schemes for shallow water equations with Coriolis source term
In this talk, we are interested in the numerical simulation of free surface geophysical flows at large scale where Coriolis effects become dominant. At this scale an efficient discretization of the so-called geostrophic equilibrium, which is characterized by the balance between the pressure gradient and the Coriolis force, is fundamental to achieve accurate numerical simulations [1, 2]. For short times, the linearized system associated to the fluid equations is the wave equation with Coriolis source term. As a first step, we study this case, in 1d and in 2d. Thanks to a Hodge type decomposition, we exhibit the kernel of the continuous operator and the behavior of the solution near this kernel. Then, extending the work initiated by Dellacherie and coauthors [3, 4] in the context of low Mach number flows, we study some Godunov type finite volume schemes obtained by modifying the numerical viscosity. In particular, we pay attention to the analysis of the discrete kernel and to the overall stability of the schemes. Some numerical results for linear wave equations and for nonlinear shallow water systems illustrate the purpose.
[1] F. Bouchut, Le Sommer et al. Frontal geostrophic adjustment and nonlinear wave phenomena in one-dimensional rotating shallow water. II. High-resolution numerical simulations, JFM 514 (2004).
[2] M. Lukacova-Medvidova, Noelle et al. Well-balanced finite volume evolution Galerkin methods for the shallow water equations, JCP 221 (2007).
[3] S. Dellacherie. Analysis of Godunov type schemes applied to the compressible Euler system at low Mach number, JCP 229 (2010).
[4] S. Dellacherie, Jung et al. Preliminary results for the study of the Godunov Scheme Applied to the Linear Wave Equation with Porosity at Low Mach Number, ESAIM ProcS 52 (2015).
Analysis of Block-Jacobi Preconditioners for Local Multi-Trace Formulations
Local Multi-Trace Formulations (local MTF) are block-sparse boundary
integral equations adapted to elliptic PDEs with piece-wise constant
coefficients (typically multi-subdomain scattering problems) only
recently introduced in [Hiptmair & Jerez-Hanckes, 2012]. In these
formulations, transmission conditions are enforced by means of local
operators, so that only adjacent subdomains communicate. Although they
provide an appealing framework for domain decomposition, present
literature only offers two contributions in this direction. In
[Hiptmair, Jerez-Hanckes, Lee, Peng, 2013] a new version of local MTF is
proposed that involves a relaxation parameter in the enforcement of
transmission conditions. In [Dolean & Gander, 2014] the authors conduct
a basic explicit study of this modified local MTF in a 1-D setting with
2 subdomains and determine a critical value for the relaxation parameter
that minimises the spectral radius of block-Jacobi iteration operators.
In the present talk, we describe new contributions extending these
results to arbitrary geometrical settings in 2-D and 3-D, assuming that
the subdomain partition does not involve any junction point.
Wednesday, August 17, 9:00 AM
Yvan Fournier (EDF)
Evolution of EDF's Code Saturne industrial CFD tool: numerical and HPC-oriented aspects
The Code Saturne CFD tool been developed by EDF, with some partner contributions, since 1997. Based on a collocated finite-volume scheme with fractional time-stepping, its main applications are incompressible turbulent flows, so development has historically focused around those aspects. In this presentation, we will describe applications, design choices, and their relation to performance and robustness aspects. Finally, we will focus on subjects of current research and planned future directions.
Bumblebees in turbulence: massively parallel numerical simulations
Insects fly even under heavy turbulent air flow conditions. To
understand the impact of turbulent fluctuations on the aerodynamics of
flapping wings, we model a bumblebee with fixed body and prescribed
wing motion, flying in a numerical wind tunnel. The inflow condition
of the tunnel varies from unperturbed laminar to strongly
turbulent. Massively parallel simulations show that turbulence does
not significantly alter the wing's leading edge vortex that is required for elevated lift production.
Mean flight forces, moments and aerodynamic power expenditures are thus unaffected, suggesting little significance of turbulence on overall flight performance in insects. The increase in variance of the aerodynamic measures with increasing turbulence intensity, however, leads to flight instabilities in freely flying animals. This work is joint work with Thomas Engels, Dmitry Kolomeskiy, Fritz-Olaf Lehmann and Jorn Sesterhenn.
Le calcul haute performance a l'Andra, defis et mise en oeuvre
Tuesday, August 23, 9:00 AM
Olivier Pironneau (LJLL/UPMC)
New and Renewed Methods for Fluid-Structured-Interactions
At the forefront of numerical methods for large displacement structured in fluids are two methods: IBM (Immersed Boundary Methods), for which Daniele Boffi and team at Pavia have obtained error estimations and MEM (Monolithic Eulerian Methods) studied by Rannacher's group at Heidelberg to which I recently contributed as well. I will present briefly these methods along with the more classic ALE methods, compare them and then discuss MEM with more details and if time allows how to make a parallel computing implementation with freefem++.
The sparse cardinal sine decomposition and applications
When solving wave scattering problems with the Boundary Element Method (BEM), one usually faces the problem of storing a dense matrix of huge size which size is proportional to the (square of) the number N of unknowns on the boundary of the scattering object. Several methods, among which the Fast Multipole Method (FMM) or the H-matrices are celebrated, were developed to circumvent this obstruction. In both cases an approximation of the matrix is obtained with a O(N log(N)) storage and the matrix-vector product has the same complexity. This permits to solve the problem, replacing the direct solver with an iterative method.
The aim of the talk is to present an alternative method which is based on an accurate version of the Fourier based convolution. Based on the non-uniform FFT, the method, called the sparse cardinal sine decomposition (SCSD) ends up to have the same complexity than the FMM for much less complexity in the implementation. We show in practice how the method works, and give applications in as different domains as Laplace, Helmholtz, Maxwell or Stokes equations.
This is a joint work with Matthieu Aussal.