Commit 245df8f1 authored by ph's avatar ph

up

parent 2f852a40
#LyX 2.3 created this file. For more info see http://www.lyx.org/
\lyxformat 544
#LyX 2.2 created this file. For more info see http://www.lyx.org/
\lyxformat 508
\begin_document
\begin_header
\save_transient_properties true
......@@ -43,6 +43,9 @@
%\newcommand{\n}{\ensuremath{\vec n}\xspace}
%\newcommand{\x}{\ensuremath{\vec x}\xspace}
\providecommand{\pgfsyspdfmark}[3]{}
% Added by lyx2lyx
\renewcommand{\textendash}{--}
\renewcommand{\textemdash}{---}
\end_preamble
\use_default_options false
\begin_modules
......@@ -64,8 +67,6 @@ figs-within-sections
\font_osf false
\font_sf_scale 100 100
\font_tt_scale 100 100
\use_microtype false
\use_dash_ligatures true
\graphics default
\default_output_format default
\output_sync 0
......@@ -95,7 +96,6 @@ figs-within-sections
\suppress_date false
\justification true
\use_refstyle 0
\use_minted 0
\index Index
\shortcut idx
\color #008000
......@@ -108,10 +108,7 @@ figs-within-sections
\tocdepth 3
\paragraph_separation skip
\defskip smallskip
\is_math_indent 0
\math_numbering_side default
\quotes_style english
\dynamic_quotes 0
\quotes_language english
\papercolumns 1
\papersides 1
\paperpagestyle default
......@@ -186,7 +183,6 @@ The MagnetoHydroDynamic (MHD) system is a fundamental model used in many
\begin_inset CommandInset citation
LatexCommand cite
key "dedner2002hyperbolic"
literal "true"
\end_inset
......@@ -201,7 +197,6 @@ We propose a simple scheme, based on an abstract kinetic interpretation,
\begin_inset CommandInset citation
LatexCommand cite
key "bouchut1999construction"
literal "true"
\end_inset
......@@ -209,7 +204,6 @@ literal "true"
\begin_inset CommandInset citation
LatexCommand cite
key "aregba2000discrete"
literal "true"
\end_inset
......@@ -225,7 +219,6 @@ literal "true"
\begin_inset CommandInset citation
LatexCommand cite
key "badwaik2018task,coulette2019high"
literal "true"
\end_inset
......@@ -387,7 +380,6 @@ We consider the MHD equations with Divergence Cleaning
\begin_inset CommandInset citation
LatexCommand cite
key "dedner2002hyperbolic"
literal "true"
\end_inset
......@@ -480,7 +472,6 @@ and the potential
\begin_inset CommandInset citation
LatexCommand cite
key "powell94,dedner2002hyperbolic,barth2006role"
literal "true"
\end_inset
......@@ -507,7 +498,6 @@ Theoretically, the parameter
\begin_inset CommandInset citation
LatexCommand cite
key "dedner2002hyperbolic"
literal "true"
\end_inset
......@@ -662,7 +652,6 @@ textcolor{blue}
\begin_inset CommandInset citation
LatexCommand cite
key "dedner2002hyperbolic"
literal "true"
\end_inset
......@@ -674,7 +663,6 @@ literal "true"
\begin_inset CommandInset citation
LatexCommand cite
key "dumbserJCP2016"
literal "true"
\end_inset
......@@ -774,7 +762,6 @@ The Lattice-Boltzmann Method (LBM) originated from the physical kinetic
\begin_inset CommandInset citation
LatexCommand cite
key "chen1998lattice"
literal "true"
\end_inset
......@@ -789,7 +776,6 @@ s can take a few number of given values.
\begin_inset CommandInset citation
LatexCommand cite
key "succi2001lattice"
literal "true"
\end_inset
......@@ -801,7 +787,6 @@ literal "true"
\begin_inset CommandInset citation
LatexCommand cite
key "bouchut1999construction,aregba2000discrete,dellar2002lattice,graille2014approximation"
literal "true"
\end_inset
......@@ -813,7 +798,6 @@ literal "true"
\begin_inset CommandInset citation
LatexCommand cite
key "badwaik:hal-01451393,coulette2016palindromic"
literal "true"
\end_inset
......@@ -1078,7 +1062,6 @@ It is a simple projection on the Maxwellian state associated to the conservative
\begin_inset CommandInset citation
LatexCommand cite
key "dellar2013interpretation"
literal "true"
\end_inset
......@@ -1297,7 +1280,6 @@ It is possible to add a small dissipation
\begin_inset CommandInset citation
LatexCommand cite
key "graille2014approximation"
literal "true"
\end_inset
......@@ -1305,7 +1287,6 @@ literal "true"
\begin_inset CommandInset citation
LatexCommand cite
key "coulette2016palindromic"
literal "true"
\end_inset
......@@ -1354,7 +1335,6 @@ For the moment, we have assumed periodic boundary conditions.
\begin_inset CommandInset citation
LatexCommand cite
key "drui2019analysis"
literal "true"
\end_inset
......@@ -1458,7 +1438,6 @@ The proof is based on standard Taylor expansions.
\begin_inset CommandInset citation
LatexCommand cite
key "courtes2020vectorial"
literal "true"
\end_inset
......@@ -1469,7 +1448,6 @@ literal "true"
\begin_inset CommandInset citation
LatexCommand cite
key "dubois2008equivalent,otomo2017two"
literal "true"
\end_inset
......@@ -1874,7 +1852,6 @@ OpenCL runtime
\begin_inset CommandInset citation
LatexCommand cite
key "klockner2012pycuda"
literal "true"
\end_inset
......@@ -1900,7 +1877,6 @@ OpenCL is practically available since september 2009.
\begin_inset CommandInset citation
LatexCommand cite
key "gaster2012heterogeneous"
literal "true"
\end_inset
......@@ -2079,7 +2055,6 @@ For more details on OpenCL, we refer for instance to
\begin_inset CommandInset citation
LatexCommand cite
key "gaster2012heterogeneous,klockner2012pycuda"
literal "true"
\end_inset
......@@ -2727,7 +2702,6 @@ The smooth vortex test is a classical test for MHD codes.
\begin_inset CommandInset citation
LatexCommand cite
key "dumbserJCP2016"
literal "true"
\end_inset
......@@ -2784,12 +2758,12 @@ The computational domain is the square
\end_inset
, with
\begin_inset Formula $L=10$
\begin_inset Formula $L=20$
\end_inset
.
We compute the solution at time
\begin_inset Formula $t=5$
\begin_inset Formula $t=10$
\end_inset
.
......@@ -2815,7 +2789,7 @@ The computational domain is the square
\begin_inset Formula $e_{N}$
\end_inset
in the normalized
in the
\begin_inset Formula $L^{1}$
\end_inset
......@@ -2824,7 +2798,7 @@ The computational domain is the square
would give similar results):
\begin_inset Formula
\[
e_{N}=\frac{\int_{\Omega}\left|(\rho u_{1})_{\text{num}}-(\rho u_{1})_{\text{exact}}\right|}{L^{2}}.
e_{N}=\int_{\Omega}\left|(\rho u_{1})_{\text{num}}-(\rho u_{1})_{\text{exact}}\right|.
\]
\end_inset
......@@ -2841,9 +2815,6 @@ The obtained numerical results are summed up in Table
\begin_inset CommandInset ref
LatexCommand ref
reference "tab:Convergence-and-performance"
plural "false"
caps "false"
noprefix "false"
\end_inset
......@@ -2867,15 +2838,13 @@ status open
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="6" columns="7">
<lyxtabular version="3" rows="6" columns="5">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
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<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
......@@ -2911,31 +2880,13 @@ N
512
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
1024
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\begin_inset Text
\begin_layout Plain Layout
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......@@ -2976,24 +2927,6 @@ N
\end_layout
\end_inset
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......@@ -3041,24 +2974,6 @@ N
\end_layout
\end_inset
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
......@@ -3085,7 +3000,7 @@ GPU
\begin_inset Text
\begin_layout Plain Layout
0.04s
\end_layout
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......@@ -3094,7 +3009,7 @@ GPU
\begin_inset Text
\begin_layout Plain Layout
0.31s
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......@@ -3103,25 +3018,7 @@ GPU
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2.46s
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\end_inset
......@@ -3130,7 +3027,7 @@ GPU
\begin_inset Text
\begin_layout Plain Layout
19.48s
\end_layout
\end_inset
......@@ -3157,7 +3054,7 @@ GPU
\begin_inset Text
\begin_layout Plain Layout
0.0506727
\end_layout
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......@@ -3166,7 +3063,7 @@ GPU
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0.0130625
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......@@ -3175,25 +3072,7 @@ GPU
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0.00349523
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......@@ -3202,7 +3081,7 @@ GPU
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......@@ -3227,25 +3106,7 @@ conv.
\begin_inset Text
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-
\end_layout
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......@@ -3254,7 +3115,7 @@ conv.
\begin_inset Text
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1.96
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\end_inset
......@@ -3263,7 +3124,7 @@ conv.
\begin_inset Text
\begin_layout Plain Layout
1.90
\end_layout
\end_inset
......@@ -3272,7 +3133,7 @@ conv.
\begin_inset Text
\begin_layout Plain Layout
0.93
\end_layout
\end_inset
......@@ -3319,7 +3180,6 @@ The Orszag Tang test case
\begin_inset CommandInset citation
LatexCommand cite
key "orszag1979small,dahlburg89orszag,picone91orszag"
literal "true"
\end_inset
......@@ -4173,7 +4033,6 @@ The tilt instability has been studied in
\begin_inset CommandInset citation
LatexCommand cite
key "richard1990tilt,strauss1998adaptive,lankalapalli2007adaptive"
literal "true"
\end_inset
......@@ -4213,7 +4072,6 @@ reference "fig:current-3"
\begin_inset CommandInset citation
LatexCommand cite
key "richard1990tilt,baty2019finmhd"
literal "true"
\end_inset
......@@ -4222,7 +4080,6 @@ literal "true"
\begin_inset CommandInset citation
LatexCommand cite
key "richard1990tilt,keppens2014interacting"
literal "true"
\end_inset
......@@ -4231,7 +4088,6 @@ literal "true"
\begin_inset CommandInset citation
LatexCommand cite
key "strauss1998adaptive,lankalapalli2007adaptive"
literal "true"
\end_inset
......@@ -4878,7 +4734,6 @@ Currents sheets develop at the edges of the magnetic islands.
\begin_inset CommandInset citation
LatexCommand cite
key "lankalapalli2007adaptive"
literal "true"
\end_inset
......@@ -4925,7 +4780,6 @@ reference "fig:current-conv"
\begin_inset CommandInset citation
LatexCommand cite
key "lankalapalli2007adaptive"
literal "true"
\end_inset
......@@ -4943,7 +4797,6 @@ literal "true"
\begin_inset CommandInset citation
LatexCommand cite
key "lankalapalli2007adaptive"
literal "true"
\end_inset
......@@ -5304,7 +5157,6 @@ During the development of the instability, the kinetic energy of the system
\begin_inset CommandInset citation
LatexCommand cite
key "richard1990tilt"
literal "true"
\end_inset
......@@ -5312,7 +5164,6 @@ literal "true"
\begin_inset CommandInset citation
LatexCommand cite
key "lankalapalli2007adaptive"
literal "true"
\end_inset
......@@ -5321,7 +5172,6 @@ literal "true"
\begin_inset CommandInset citation
LatexCommand cite
key "richard1990tilt"
literal "true"
\end_inset
......@@ -5343,7 +5193,6 @@ literal "true"
\begin_inset CommandInset citation
LatexCommand cite
key "lankalapalli2007adaptive"
literal "true"
\end_inset
......@@ -5498,7 +5347,6 @@ reference "fig:kinetic-2"
\begin_inset CommandInset citation
LatexCommand cite
key "richard1990tilt"
literal "true"
\end_inset
......@@ -5506,7 +5354,6 @@ literal "true"
\begin_inset CommandInset citation
LatexCommand cite
key "lankalapalli2007adaptive"
literal "true"
\end_inset
......@@ -5515,7 +5362,6 @@ literal "true"
\begin_inset CommandInset citation
LatexCommand cite
key "keppens2014interacting"
literal "true"
\end_inset
......@@ -6271,7 +6117,6 @@ Now, the order of resolution is
\begin_inset CommandInset citation
LatexCommand cite
key "dedner2002hyperbolic"
literal "true"
\end_inset
......@@ -6794,7 +6639,6 @@ When conducting the simulations, we observed that the limiting factor was
\begin_inset CommandInset citation
LatexCommand cite
key "bramas2020optimization"
literal "true"
\end_inset
......
......@@ -191,7 +191,7 @@ void exact_smooth_vortex(real *x, real t, real *w) {
const real bref = 0.2;
const real mu = 1;
const real udrift[2] = {1.0, 1.0};
const real xstart[2] = {5., 5.};
const real xstart[2] = {10., 10.};
//
real xrel[3] = {x[0] - uref * udrift[0] * t - xstart[0],
x[1] - uref * udrift[1] * t - xstart[1], 0.0};
......
......@@ -42,13 +42,13 @@ _maxplot = 0.45
_nx = 256
_ny = 256
_Lx = 10 # 12 #6 #1
_Ly = 10 # 12 #6 #1
_Lx = 20 # 12 #6 #1
_Ly = 20 # 12 #6 #1
# transport velocity
vel = np.array([1., 1.])
_Tmax = 5
_Tmax = 10
def solve_ocl(m=_m, n=_n, nx=_nx, ny=_ny, Lx=_Lx, Ly=_Ly, Tmax=_Tmax,
......@@ -189,7 +189,7 @@ def solve_ocl(m=_m, n=_n, nx=_nx, ny=_ny, Lx=_Lx, Ly=_Ly, Tmax=_Tmax,
exit(f"Nan in kinetic_cpu at ite {ite}")
else:
#print("t=",t," L2 norm =", np.sqrt(np.sum(kinetic_cpu)/Lx/Ly))
print("t=",t," L1 norm =", np.sum(kinetic_cpu)/Lx/Ly)
print("t=",t," L1 norm =", np.sum(kinetic_cpu))
else:
print(ite_title, end='\r')
......
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